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{
"cells": [
{
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"id": "db451ca7-24c4-4875-98cc-8da35f0e1a5a",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"import logging\n",
"\n",
"logging.basicConfig()\n",
"logging.getLogger('metaanalyser').setLevel(level=logging.DEBUG)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "03e1416c-d889-4126-b8f0-5bfa197f3244",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"from langchain.chat_models import ChatOpenAI\n",
"\n",
"llm = ChatOpenAI(temperature=0)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "a75a92f5-ccc3-4296-90bf-f2a2f976099c",
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{
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"text": [
"INFO:metaanalyser.chains.sr:Searching `Pitman-Yor Language Model` on Google Scholar.\n",
"INFO:metaanalyser.paper.paper:Looking for `Pitman-Yor Language Model` on Google Scholar, offset: 0...\n"
]
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{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"\u001b[1m> Entering new SRChain chain...\u001b[0m\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:metaanalyser.paper.paper:Looking for `Pitman-Yor Language Model` on Google Scholar, offset: 10...\n",
"INFO:metaanalyser.paper.paper:Looking for `Pitman-Yor Language Model` on Google Scholar, offset: 20...\n",
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"INFO:metaanalyser.paper.paper:Collecting details...\n"
]
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"0it [00:00, ?it/s]"
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"WARNING:metaanalyser.paper.paper:Category 62G07, 62H30 is not found in CATEGORY_NAME_ID_MAP.\n",
"WARNING:metaanalyser.paper.paper:Category G.3.7 is not found in CATEGORY_NAME_ID_MAP.\n",
"INFO:metaanalyser.chains.sr:Writing an overview of the paper.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"\u001b[1m> Entering new SROverviewChain chain...\u001b[0m\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:metaanalyser.paper.paper:Number of papers: 8, number of tokens: 1480, text: Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Summry: We introduce the Pitman Yor Diffusion Tree ...\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Prompt after formatting:\n",
"\u001b[32;1m\u001b[1;3mSystem: You are a research scientist and intereseted in Machine Learning, Computation and Language and Statistics Theory. You are working on writing a systematic review regarding \"Pitman-Yor Language Model\".\n",
"Human: Write an overview of the systematic review based on the summary of the following list of paper abstracts.\n",
"\n",
"-----\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Summry: We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model and then present two inference methods: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary.\n",
"\n",
"\n",
"Title: Assessing language models with scaling properties\n",
"citation_id: 2\n",
"Summry: Language models have primarily been evaluated with perplexity. While perplexity quantifies the most comprehensible prediction performance, it does not provide qualitative information on the success or failure of models. Another approach for evaluating language models is thus proposed, using the scaling properties of natural language. Five such tests are considered, with the first two accounting for the vocabulary population and the other three for the long memory of natural language. The following models were evaluated with these tests: n-grams, probabilistic context-free grammar (PCFG), Simon and Pitman-Yor (PY) processes, hierarchical PY, and neural language models. Only the neural language models exhibit the long memory properties of natural language, but to a limited degree. The effectiveness of every test of these models is also discussed.\n",
"\n",
"\n",
"Title: Heavy-Tailed Pitman--Yor Mixture Models\n",
"citation_id: 3\n",
"Summry: Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability measures such as the Dirichlet process. The first contribution of this paper focuses on the characterization of the tails of the so-called Pitman--Yor process, which includes the Dirichlet process as a particular case. We show that the right tail of a Pitman--Yor process, known as the stable law process, is heavy-tailed, provided that the centering distribution is itself heavy-tailed. A second contribution of the paper rests on the development of two classes of heavy-tailed mixture models and the assessment of their relative merits. Multivariate extensions of the proposed heavy-tailed mixtures are here devised along with a predictor-dependent version so to learn about the effect of covariates on a multivariate heavy-tailed response. The simulation study suggests that the proposed method performs well in a variety of scenarios, and we showcase the application of the proposed methods in a neuroscience dataset.\n",
"\n",
"\n",
"Title: Empirical and Full Bayes estimation of the type of a Pitman-Yor process\n",
"citation_id: 4\n",
"Summry: The Pitman-Yor process is a random discrete probability distribution of which the atoms can be used to model the relative abundance of species. The process is indexed by a type parameter $\\sigma$, which controls the number of different species in a finite sample from a realization of the distribution. A random sample of size $n$ from the Pitman-Yor process of type $\\sigma>0$ will contain of the order $n^\\sigma$ distinct values (``species''). In this paper we consider the estimation of the type parameter by both empirical Bayes and full Bayes methods. We derive the asymptotic normality of the empirical Bayes estimator and a Bernstein-von Mises theorem for the full Bayes posterior, in the frequentist setup that the observations are a random sample from a given true distribution. We also consider the estimation of the second parameter of the Pitman-Yor process, the prior precision. We apply our results to derive the limit behaviour of the likelihood ratio in a setting of forensic statistics.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 5\n",
"Summry: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 6\n",
"Summry: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: Joint space neural probabilistic language model for statistical machine translation\n",
"citation_id: 7\n",
"Summry: A neural probabilistic language model (NPLM) provides an idea to achieve the better perplexity than n-gram language model and their smoothed language models. This paper investigates application area in bilingual NLP, specifically Statistical Machine Translation (SMT). We focus on the perspectives that NPLM has potential to open the possibility to complement potentially `huge' monolingual resources into the `resource-constraint' bilingual resources. We introduce an ngram-HMM language model as NPLM using the non-parametric Bayesian construction. In order to facilitate the application to various tasks, we propose the joint space model of ngram-HMM language model. We show an experiment of system combination in the area of SMT. One discovery was that our treatment of noise improved the results 0.20 BLEU points if NPLM is trained in relatively small corpus, in our case 500,000 sentence pairs, which is often the case due to the long training time of NPLM.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Summry: We propose a simple, scalable, fully generative model for transition-based dependency parsing with high accuracy. The model, parameterized by Hierarchical Pitman-Yor Processes, overcomes the limitations of previous generative models by allowing fast and accurate inference. We propose an efficient decoding algorithm based on particle filtering that can adapt the beam size to the uncertainty in the model while jointly predicting POS tags and parse trees. The UAS of the parser is on par with that of a greedy discriminative baseline. As a language model, it obtains better perplexity than a n-gram model by performing semi-supervised learning over a large unlabelled corpus. We show that the model is able to generate locally and syntactically coherent sentences, opening the door to further applications in language generation.\n",
"-----\n",
"\n",
"This overview should serve as a compass for you as you construct the outline of the systematic review and write down its details.\n",
"\n",
"Assuming that the readers of this systematic review will not be familiar with the field. In order to make it easy for readers who are not familiar with this field to understand, list the main points briefly (approximately 30 words maximum) based on the following points.\n",
"\n",
"- Motivation for this field and the problem this field are trying to solve\n",
"- Historical background of this field\n",
"- Future development of this field\n",
"\n",
"Based on these main points, provide an overview of the systematic review regarding Pitman-Yor Language Model you will write.\n",
"\n",
"Finally, write the title of the systematic review you are going to write based on this overview.\n",
"\n",
"The output should be formatted as a JSON instance that conforms to the JSON schema below.\n",
"\n",
"As an example, for the schema {\"properties\": {\"foo\": {\"title\": \"Foo\", \"description\": \"a list of strings\", \"type\": \"array\", \"items\": {\"type\": \"string\"}}}, \"required\": [\"foo\"]}}\n",
"the object {\"foo\": [\"bar\", \"baz\"]} is a well-formatted instance of the schema. The object {\"properties\": {\"foo\": [\"bar\", \"baz\"]}} is not well-formatted.\n",
"\n",
"Here is the output schema:\n",
"```\n",
"{\"properties\": {\"title\": {\"title\": \"Title\", \"description\": \"title of the systematic review\", \"type\": \"string\"}, \"main_points\": {\"title\": \"Main Points\", \"description\": \"main points that make up the systematic review\", \"type\": \"array\", \"items\": {\"type\": \"string\"}}, \"overview\": {\"title\": \"Overview\", \"description\": \"overview of the systematic review\", \"type\": \"string\"}}, \"required\": [\"title\", \"main_points\", \"overview\"]}\n",
"```\u001b[0m\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:metaanalyser.chains.base:LLM utilization: {'token_usage': {'prompt_tokens': 1921, 'completion_tokens': 180, 'total_tokens': 2101}, 'model_name': 'gpt-3.5-turbo'}\n",
"INFO:metaanalyser.chains.sr:Building the outline of the paper.\n",
"INFO:metaanalyser.paper.paper:Number of papers: 8, number of tokens: 1480, text: Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Summry: We introduce the Pitman Yor Diffusion Tree ...\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\u001b[1m> Finished chain.\u001b[0m\n",
"\n",
"\n",
"\u001b[1m> Entering new SROutlintChain chain...\u001b[0m\n",
"Prompt after formatting:\n",
"\u001b[32;1m\u001b[1;3mSystem: You are a research scientist and intereseted in Machine Learning, Computation and Language and Statistics Theory. You are working on writing a systematic review regarding \"Pitman-Yor Language Model\".\n",
"Human: Build an outline of the systematic review regarding \"Pitman-Yor Language Model\" based on the following list of paper abstracts.\n",
"\n",
"-----\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Summry: We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model and then present two inference methods: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary.\n",
"\n",
"\n",
"Title: Assessing language models with scaling properties\n",
"citation_id: 2\n",
"Summry: Language models have primarily been evaluated with perplexity. While perplexity quantifies the most comprehensible prediction performance, it does not provide qualitative information on the success or failure of models. Another approach for evaluating language models is thus proposed, using the scaling properties of natural language. Five such tests are considered, with the first two accounting for the vocabulary population and the other three for the long memory of natural language. The following models were evaluated with these tests: n-grams, probabilistic context-free grammar (PCFG), Simon and Pitman-Yor (PY) processes, hierarchical PY, and neural language models. Only the neural language models exhibit the long memory properties of natural language, but to a limited degree. The effectiveness of every test of these models is also discussed.\n",
"\n",
"\n",
"Title: Heavy-Tailed Pitman--Yor Mixture Models\n",
"citation_id: 3\n",
"Summry: Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability measures such as the Dirichlet process. The first contribution of this paper focuses on the characterization of the tails of the so-called Pitman--Yor process, which includes the Dirichlet process as a particular case. We show that the right tail of a Pitman--Yor process, known as the stable law process, is heavy-tailed, provided that the centering distribution is itself heavy-tailed. A second contribution of the paper rests on the development of two classes of heavy-tailed mixture models and the assessment of their relative merits. Multivariate extensions of the proposed heavy-tailed mixtures are here devised along with a predictor-dependent version so to learn about the effect of covariates on a multivariate heavy-tailed response. The simulation study suggests that the proposed method performs well in a variety of scenarios, and we showcase the application of the proposed methods in a neuroscience dataset.\n",
"\n",
"\n",
"Title: Empirical and Full Bayes estimation of the type of a Pitman-Yor process\n",
"citation_id: 4\n",
"Summry: The Pitman-Yor process is a random discrete probability distribution of which the atoms can be used to model the relative abundance of species. The process is indexed by a type parameter $\\sigma$, which controls the number of different species in a finite sample from a realization of the distribution. A random sample of size $n$ from the Pitman-Yor process of type $\\sigma>0$ will contain of the order $n^\\sigma$ distinct values (``species''). In this paper we consider the estimation of the type parameter by both empirical Bayes and full Bayes methods. We derive the asymptotic normality of the empirical Bayes estimator and a Bernstein-von Mises theorem for the full Bayes posterior, in the frequentist setup that the observations are a random sample from a given true distribution. We also consider the estimation of the second parameter of the Pitman-Yor process, the prior precision. We apply our results to derive the limit behaviour of the likelihood ratio in a setting of forensic statistics.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 5\n",
"Summry: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 6\n",
"Summry: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: Joint space neural probabilistic language model for statistical machine translation\n",
"citation_id: 7\n",
"Summry: A neural probabilistic language model (NPLM) provides an idea to achieve the better perplexity than n-gram language model and their smoothed language models. This paper investigates application area in bilingual NLP, specifically Statistical Machine Translation (SMT). We focus on the perspectives that NPLM has potential to open the possibility to complement potentially `huge' monolingual resources into the `resource-constraint' bilingual resources. We introduce an ngram-HMM language model as NPLM using the non-parametric Bayesian construction. In order to facilitate the application to various tasks, we propose the joint space model of ngram-HMM language model. We show an experiment of system combination in the area of SMT. One discovery was that our treatment of noise improved the results 0.20 BLEU points if NPLM is trained in relatively small corpus, in our case 500,000 sentence pairs, which is often the case due to the long training time of NPLM.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Summry: We propose a simple, scalable, fully generative model for transition-based dependency parsing with high accuracy. The model, parameterized by Hierarchical Pitman-Yor Processes, overcomes the limitations of previous generative models by allowing fast and accurate inference. We propose an efficient decoding algorithm based on particle filtering that can adapt the beam size to the uncertainty in the model while jointly predicting POS tags and parse trees. The UAS of the parser is on par with that of a greedy discriminative baseline. As a language model, it obtains better perplexity than a n-gram model by performing semi-supervised learning over a large unlabelled corpus. We show that the model is able to generate locally and syntactically coherent sentences, opening the door to further applications in language generation.\n",
"-----\n",
"\n",
"The following is an overview of this systematic review. Build the outline of the systematic review according to this overview.\n",
"\n",
"-----\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"Points:\n",
" - Motivation: Pitman-Yor Language Model for Machine Learning, Computation, and Language and Statistics Theory\n",
" - Historical background: Introduction of Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering\n",
" - Future development: Potential applications in nonparametric clustering of data and generative transition-based dependency parsing\n",
"Overview: This systematic review provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing. We discuss the historical background of the model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering. We also explore potential future developments, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
"-----\n",
"\n",
"Device each section of this outline by citing abstracts from the papers.\n",
"The beginning of element of the sections should by titled \"Introduction\" and last element of the sections should be titled \"Conclusion\".\n",
"It is preferred that sections be divided into more child sections. Each section can have up to two child sections.\n",
"\n",
"The output should be formatted as a JSON instance that conforms to the JSON schema below.\n",
"\n",
"As an example, for the schema {\"properties\": {\"foo\": {\"title\": \"Foo\", \"description\": \"a list of strings\", \"type\": \"array\", \"items\": {\"type\": \"string\"}}}, \"required\": [\"foo\"]}}\n",
"the object {\"foo\": [\"bar\", \"baz\"]} is a well-formatted instance of the schema. The object {\"properties\": {\"foo\": [\"bar\", \"baz\"]}} is not well-formatted.\n",
"\n",
"Here is the output schema:\n",
"```\n",
"{\"properties\": {\"sections\": {\"title\": \"Sections\", \"description\": \"sections that make up this systematic review\", \"type\": \"array\", \"items\": {\"$ref\": \"#/definitions/Section\"}}, \"citations_ids\": {\"title\": \"Citations Ids\", \"description\": \"citation ids to all paper abstracts cited in this paper\", \"type\": \"array\", \"items\": {\"type\": \"integer\"}}}, \"required\": [\"sections\", \"citations_ids\"], \"definitions\": {\"Section\": {\"title\": \"Section\", \"type\": \"object\", \"properties\": {\"title\": {\"title\": \"Title\", \"description\": \"title of this section\", \"type\": \"string\"}, \"children\": {\"title\": \"Children\", \"description\": \"subsections of this section\", \"type\": \"array\", \"items\": {\"$ref\": \"#/definitions/Section\"}}, \"description\": {\"title\": \"Description\", \"description\": \"brief description of this section (approximately 30 words maximum)\", \"type\": \"string\"}, \"citation_ids\": {\"title\": \"Citation Ids\", \"description\": \"citation ids to a paper abstract that this section cites\", \"type\": \"array\", \"items\": {\"type\": \"integer\"}}}, \"required\": [\"title\", \"description\", \"citation_ids\"]}}}\n",
"```\u001b[0m\n"
]
},
{
"name": "stderr",
"output_type": "stream",
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"INFO:metaanalyser.chains.base:LLM utilization: {'token_usage': {'prompt_tokens': 2196, 'completion_tokens': 454, 'total_tokens': 2650}, 'model_name': 'gpt-3.5-turbo'}\n",
"INFO:metaanalyser.chains.sr:Creating vector store.\n"
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{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\u001b[1m> Finished chain.\u001b[0m\n"
]
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"name": "stderr",
"output_type": "stream",
"text": [
"INFO:metaanalyser.paper.vectorstore:Creating vector store, tiktoken_encoder_model_name='gpt-3.5-turbo', chunk_size=150, chunk_overlap=10\n"
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"INFO:metaanalyser.paper.vectorstore:Vector store is created from 10 papers, document size=1014\n",
"INFO:metaanalyser.chains.sr:Writing sections: [1 / 7]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"\u001b[1m> Entering new SRSectionChain chain...\u001b[0m\n",
"Prompt after formatting:\n",
"\u001b[32;1m\u001b[1;3mSystem: You are a research scientist and intereseted in Machine Learning, Computation and Language and Statistics Theory. You are working on writing a systematic review regarding \"Pitman-Yor Language Model\".\n",
"\n",
"The outline of the systematic review is as follows:\n",
"\n",
"-----\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"1. Introduction: This section provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing.\n",
"2. Historical Background: This section discusses the historical background of the Pitman-Yor Language Model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
" 1. Pitman Yor Diffusion Tree: This subsection discusses the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
"3. Future Development: This section explores potential future developments of the Pitman-Yor Language Model, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
" 1. Nonparametric Clustering of Data: This subsection discusses the potential application of the Pitman-Yor Language Model in nonparametric clustering of data.\n",
" 2. Generative Transition-Based Dependency Parsing: This subsection discusses the potential application of the Pitman-Yor Language Model in generative transition-based dependency parsing.\n",
"4. Conclusion: This systematic review provides an overview of the Pitman-Yor Language Model, its historical background, and potential future developments.\n",
"Human: Write the \"Introduction\" section of this systematic review based on the following list of snippets or abstracts of relative papers.\n",
"\n",
"-----\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model and then present two inference methods: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary.\n",
"\n",
"\n",
"Title: Assessing language models with scaling properties\n",
"citation_id: 2\n",
"Text: Language models have primarily been evaluated with perplexity. While perplexity quantifies the most comprehensible prediction performance, it does not provide qualitative information on the success or failure of models. Another approach for evaluating language models is thus proposed, using the scaling properties of natural language. Five such tests are considered, with the first two accounting for the vocabulary population and the other three for the long memory of natural language. The following models were evaluated with these tests: n-grams, probabilistic context-free grammar (PCFG), Simon and Pitman-Yor (PY) processes, hierarchical PY, and neural language models. Only the neural language models exhibit the long memory properties of natural language, but to a limited degree. The effectiveness of every test of these models is also discussed.\n",
"\n",
"\n",
"Title: Heavy-Tailed Pitman--Yor Mixture Models\n",
"citation_id: 3\n",
"Text: Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability measures such as the Dirichlet process. The first contribution of this paper focuses on the characterization of the tails of the so-called Pitman--Yor process, which includes the Dirichlet process as a particular case. We show that the right tail of a Pitman--Yor process, known as the stable law process, is heavy-tailed, provided that the centering distribution is itself heavy-tailed. A second contribution of the paper rests on the development of two classes of heavy-tailed mixture models and the assessment of their relative merits. Multivariate extensions of the proposed heavy-tailed mixtures are here devised along with a predictor-dependent version so to learn about the effect of covariates on a multivariate heavy-tailed response. The simulation study suggests that the proposed method performs well in a variety of scenarios, and we showcase the application of the proposed methods in a neuroscience dataset.\n",
"\n",
"\n",
"Title: Empirical and Full Bayes estimation of the type of a Pitman-Yor process\n",
"citation_id: 4\n",
"Text: The Pitman-Yor process is a random discrete probability distribution of which the atoms can be used to model the relative abundance of species. The process is indexed by a type parameter $\\sigma$, which controls the number of different species in a finite sample from a realization of the distribution. A random sample of size $n$ from the Pitman-Yor process of type $\\sigma>0$ will contain of the order $n^\\sigma$ distinct values (``species''). In this paper we consider the estimation of the type parameter by both empirical Bayes and full Bayes methods. We derive the asymptotic normality of the empirical Bayes estimator and a Bernstein-von Mises theorem for the full Bayes posterior, in the frequentist setup that the observations are a random sample from a given true distribution. We also consider the estimation of the second parameter of the Pitman-Yor process, the prior precision. We apply our results to derive the limit behaviour of the likelihood ratio in a setting of forensic statistics.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 5\n",
"Text: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 6\n",
"Text: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: Joint space neural probabilistic language model for statistical machine translation\n",
"citation_id: 7\n",
"Text: A neural probabilistic language model (NPLM) provides an idea to achieve the better perplexity than n-gram language model and their smoothed language models. This paper investigates application area in bilingual NLP, specifically Statistical Machine Translation (SMT). We focus on the perspectives that NPLM has potential to open the possibility to complement potentially `huge' monolingual resources into the `resource-constraint' bilingual resources. We introduce an ngram-HMM language model as NPLM using the non-parametric Bayesian construction. In order to facilitate the application to various tasks, we propose the joint space model of ngram-HMM language model. We show an experiment of system combination in the area of SMT. One discovery was that our treatment of noise improved the results 0.20 BLEU points if NPLM is trained in relatively small corpus, in our case 500,000 sentence pairs, which is often the case due to the long training time of NPLM.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: We propose a simple, scalable, fully generative model for transition-based dependency parsing with high accuracy. The model, parameterized by Hierarchical Pitman-Yor Processes, overcomes the limitations of previous generative models by allowing fast and accurate inference. We propose an efficient decoding algorithm based on particle filtering that can adapt the beam size to the uncertainty in the model while jointly predicting POS tags and parse trees. The UAS of the parser is on par with that of a greedy discriminative baseline. As a language model, it obtains better perplexity than a n-gram model by performing semi-supervised learning over a large unlabelled corpus. We show that the model is able to generate locally and syntactically coherent sentences, opening the door to further applications in language generation.\n",
"-----\n",
"\n",
"This systematic review should adhere to the following overview:\n",
"\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"Points:\n",
" - Motivation: Pitman-Yor Language Model for Machine Learning, Computation, and Language and Statistics Theory\n",
" - Historical background: Introduction of Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering\n",
" - Future development: Potential applications in nonparametric clustering of data and generative transition-based dependency parsing\n",
"Overview: This systematic review provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing. We discuss the historical background of the model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering. We also explore potential future developments, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
"\n",
"Write the \"Introduction: This section provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing.\" section with respect to this overview. Write the text in markdown format. The title of this section should bu suffixed with 2 level markdown title (`##`). The text of the section should be based on a snippet or abstact and should be clearly cited. The citation should be written at the end of the sentence in the form `[^<ID>]` where `ID` refers to the citation_id.\u001b[0m\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:metaanalyser.chains.base:LLM utilization: {'token_usage': {'prompt_tokens': 2078, 'completion_tokens': 162, 'total_tokens': 2240}, 'model_name': 'gpt-3.5-turbo'}\n",
"INFO:metaanalyser.chains.sr:Writing sections: [2 / 7]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\u001b[1m> Finished chain.\u001b[0m\n",
"\n",
"\n",
"\u001b[1m> Entering new SRSectionChain chain...\u001b[0m\n",
"Prompt after formatting:\n",
"\u001b[32;1m\u001b[1;3mSystem: You are a research scientist and intereseted in Machine Learning, Computation and Language and Statistics Theory. You are working on writing a systematic review regarding \"Pitman-Yor Language Model\".\n",
"\n",
"The outline of the systematic review is as follows:\n",
"\n",
"-----\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"1. Introduction: This section provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing.\n",
"2. Historical Background: This section discusses the historical background of the Pitman-Yor Language Model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
" 1. Pitman Yor Diffusion Tree: This subsection discusses the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
"3. Future Development: This section explores potential future developments of the Pitman-Yor Language Model, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
" 1. Nonparametric Clustering of Data: This subsection discusses the potential application of the Pitman-Yor Language Model in nonparametric clustering of data.\n",
" 2. Generative Transition-Based Dependency Parsing: This subsection discusses the potential application of the Pitman-Yor Language Model in generative transition-based dependency parsing.\n",
"4. Conclusion: This systematic review provides an overview of the Pitman-Yor Language Model, its historical background, and potential future developments.\n",
"Human: Write the \"Historical Background\" section of this systematic review based on the following list of snippets or abstracts of relative papers.\n",
"\n",
"-----\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model and then present two inference methods: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary.\n",
"\n",
"\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: Pitman-Yor Diffusion Trees David A. Knowles, Zoubin Ghahramani University of Cambridge 1 1 0 2 n u J 6 1 ] L M . t a t s [ 2 v 4 9 4 2 . 6 0 1 1 : v i X r a Abstract We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restric- tion to binary branching structure.\n",
"\n",
"\n",
"Title: Joint space neural probabilistic language model for statistical machine translation\n",
"citation_id: 7\n",
"Text: (2012), 40–51. [36] OKITA, T., AND WAY, A. Hierarchical pitman-yor language model in machine translation. In Proceedings of the International Conference on Asian Language Processing (IALP 2010) (2010). [37] OKITA, T., AND WAY, A. Pitman-Yor process-based language model for Machine Translation. International Journal on Asian Language Processing 21, 2 (2010), 57–70.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: We shall also consider unlexicalised models, based only on POS tags. 3.1 Hierarchical Pitman-Yor processes The probability distributions for predicting words, tags and transitions are drawn from hierarchical Pitmar-Yor Process (HPYP) priors. HPYP mod- els were originally proposed for n-gram language modelling (Teh, 2006), and have been applied to various NLP tasks. A version of approximate in- ference in the HPYP model recovers interpolated Kneser-Ney smoothing (Kneser and Ney, 1995), one of the best preforming n-gram language mod- els.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 9\n",
"Text: We shall also consider unlexicalised models, based only on POS tags. 3.1 Hierarchical Pitman-Yor processes The probability distributions for predicting words, tags and transitions are drawn from hierarchical Pitmar-Yor Process (HPYP) priors. HPYP mod- els were originally proposed for n-gram language modelling (Teh, 2006), and have been applied to various NLP tasks. A version of approximate in- ference in the HPYP model recovers interpolated Kneser-Ney smoothing (Kneser and Ney, 1995), one of the best preforming n-gram language mod- els.\n",
"\n",
"\n",
"Title: Assessing language models with scaling properties\n",
"citation_id: 2\n",
"Text: The basic models introduced thus far define nothing about how to introduce words: we would simply generate random sequences and examine their scaling properties, because the basic formulation thus far governs the nature of the language model elaborated from these models. By mapping a word to the elements produced, however, we would generate a language model, like the two-stage model proposed in (Goldwater et al. 2011). Here, we consider a more advanced model proposed as the hierarchical Pitman-Yor language model (HPYLM)(Teh 2006), which integrates the Pitman-Yor process into an n-gram model. 4.4 Neural Language Models\n",
"\n",
"\n",
"Title: Heavy-Tailed Pitman--Yor Mixture Models\n",
"citation_id: 3\n",
"Text: Prior to introducing the main problems to be addressed, and the main contributions of this paper, we first lay the groundwork. The Pitman–Yor process is a random probability measure that has received considerable attention in recent years (e.g. Pitman and Yor, 1997; Ishwaran and James, 2001; Teh, 2006; Bassetti et al., 2014; Miller and Harrison, 2014; Canale et al., 2017; Arbel et al., 2019; Lijoi et al., 2020; Corradin et al., 2021) and that includes the Dirichlet process as a particular case.\n",
"\n",
"\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: In ongoing work we use the PYDT to learn hierarchi- cal structure over latent variables in models including Hidden Markov Models, specifically in part of speech tagging (Kupiec, 1992) where a hierarchy over the la- tent states aids interpretability, and Latent Dirichlet Allocation, where it is intuitive that topics might be hierarchically clustered (Blei et al., 2004). Another interesting direction would be to use the prior over branching structures implied by the PYDT in the an- notated hierarchies model of Roy et al. (2007).\n",
"\n",
"\n",
"Title: Assessing language models with scaling properties\n",
"citation_id: 2\n",
"Text: 4.3 Simon/Pitman-Yor Models The Simon and Pitman-Yor (PY) processes are important for our perspective, because they are capable of reproducing Zipf’s law and Heaps’ law with simple formulations. It is thus interesting to see whether they satisfy the other scaling properties. These are generative models, and a sequence is formulated over time, either through (1) introduc- 1) be the number of word types 1. The sequence starts with tion of new words or (2) sampling from the past sequence. Let K(X t existing in X t K(X0) = 1 and X0 = x0 at t = 0.\n",
"-----\n",
"\n",
"This systematic review should adhere to the following overview:\n",
"\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"Points:\n",
" - Motivation: Pitman-Yor Language Model for Machine Learning, Computation, and Language and Statistics Theory\n",
" - Historical background: Introduction of Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering\n",
" - Future development: Potential applications in nonparametric clustering of data and generative transition-based dependency parsing\n",
"Overview: This systematic review provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing. We discuss the historical background of the model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering. We also explore potential future developments, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
"\n",
"Write the \"Historical Background: This section discusses the historical background of the Pitman-Yor Language Model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\" section with respect to this overview. Write the text in markdown format. The title of this section should bu suffixed with 2 level markdown title (`##`). The text of the section should be based on a snippet or abstact and should be clearly cited. The citation should be written at the end of the sentence in the form `[^<ID>]` where `ID` refers to the citation_id.\u001b[0m\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:metaanalyser.chains.base:LLM utilization: {'token_usage': {'prompt_tokens': 2027, 'completion_tokens': 202, 'total_tokens': 2229}, 'model_name': 'gpt-3.5-turbo'}\n",
"INFO:metaanalyser.chains.sr:Writing sections: [3 / 7]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\u001b[1m> Finished chain.\u001b[0m\n",
"\n",
"\n",
"\u001b[1m> Entering new SRSectionChain chain...\u001b[0m\n",
"Prompt after formatting:\n",
"\u001b[32;1m\u001b[1;3mSystem: You are a research scientist and intereseted in Machine Learning, Computation and Language and Statistics Theory. You are working on writing a systematic review regarding \"Pitman-Yor Language Model\".\n",
"\n",
"The outline of the systematic review is as follows:\n",
"\n",
"-----\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"1. Introduction: This section provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing.\n",
"2. Historical Background: This section discusses the historical background of the Pitman-Yor Language Model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
" 1. Pitman Yor Diffusion Tree: This subsection discusses the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
"3. Future Development: This section explores potential future developments of the Pitman-Yor Language Model, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
" 1. Nonparametric Clustering of Data: This subsection discusses the potential application of the Pitman-Yor Language Model in nonparametric clustering of data.\n",
" 2. Generative Transition-Based Dependency Parsing: This subsection discusses the potential application of the Pitman-Yor Language Model in generative transition-based dependency parsing.\n",
"4. Conclusion: This systematic review provides an overview of the Pitman-Yor Language Model, its historical background, and potential future developments.\n",
"Human: Write the \"Pitman Yor Diffusion Tree\" section of this systematic review based on the following list of snippets or abstracts of relative papers.\n",
"\n",
"-----\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model and then present two inference methods: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary.\n",
"\n",
"\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: Pitman-Yor Diffusion Trees David A. Knowles, Zoubin Ghahramani University of Cambridge 1 1 0 2 n u J 6 1 ] L M . t a t s [ 2 v 4 9 4 2 . 6 0 1 1 : v i X r a Abstract We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restric- tion to binary branching structure.\n",
"\n",
"\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: An alternative to the PYDT to obtain un- bounded trees is given by Adams et al. (2010). They use a nested stick-breaking process to construct the tree, which is then endowed with a diffusion process. Data live at internal nodes of the tree, rather than at leaves as in the PYDT. We introduce the Pitman Yor Diffusion Tree (PYDT), a generalization of the Dirichlet Diffusion Tree (Neal, 2001) to trees with arbitrary branching structure.\n",
"\n",
"\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: Our contributions are as follows. In Section 1 we describe the generative process corresponding to the PYDT. In Section 2 we derive the probability of a tree, and in Section 3 show some important properties of the process. Section 4 describes our hierarchical clustering models utilising the PYDT. In Section 5 we present an MCMC sampler and a greedy EM algorithm, which we developped for the DDT in Knowles et al. (2011). We present results demonstrating the utility of the PYDT in Section 6. In the supplementary material we de- scribe how to sample from the PYDT.\n",
"\n",
"\n",
"Title: Heavy-Tailed Pitman--Yor Mixture Models\n",
"citation_id: 3\n",
"Text: Prior to introducing the main problems to be addressed, and the main contributions of this paper, we first lay the groundwork. The Pitman–Yor process is a random probability measure that has received considerable attention in recent years (e.g. Pitman and Yor, 1997; Ishwaran and James, 2001; Teh, 2006; Bassetti et al., 2014; Miller and Harrison, 2014; Canale et al., 2017; Arbel et al., 2019; Lijoi et al., 2020; Corradin et al., 2021) and that includes the Dirichlet process as a particular case.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 5\n",
"Text: The Kernel Pitman-Yor Process Sotirios P. Chatzis, Dimitrios Korkinof, and Yiannis Demiris 1 2 1 0 2 t c O 5 1 ] G L . s c [ 1 v 4 8 1 4 . 0 1 2 1 : v i X r a Abstract—In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first intro- ducing an infinite sequence of random locations.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 6\n",
"Text: The Kernel Pitman-Yor Process Sotirios P. Chatzis, Dimitrios Korkinof, and Yiannis Demiris 1 2 1 0 2 t c O 5 1 ] G L . s c [ 1 v 4 8 1 4 . 0 1 2 1 : v i X r a Abstract—In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first intro- ducing an infinite sequence of random locations.\n",
"\n",
"\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: Qualitatively, Figure 7: Tree structure learnt for the animals dataset of Kemp and Tenenbaum (2008). we have shown the PYDT can find simpler, more in- terpretable representations of data than the DDT. To encourage the use of the PYDT by the community we will make our code publicly available.\n",
"\n",
"\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: We have shown the PYDT defines an infinitely ex- changeable distribution over data points. We demon- strated an MCMC sampler and Bayesian EM with greedy search, both using message passing on the tree structure. More advanced MCMC methods could be of use here. Quantitatively we have shown a modest improvement relative to the DDT on a density estima- tion task. However, we see improved interpretability as the key benefit of removing the restriction to binary trees, especially since hierarchical clustering is typi- cally used as a data exploration tool.\n",
"-----\n",
"\n",
"This systematic review should adhere to the following overview:\n",
"\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"Points:\n",
" - Motivation: Pitman-Yor Language Model for Machine Learning, Computation, and Language and Statistics Theory\n",
" - Historical background: Introduction of Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering\n",
" - Future development: Potential applications in nonparametric clustering of data and generative transition-based dependency parsing\n",
"Overview: This systematic review provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing. We discuss the historical background of the model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering. We also explore potential future developments, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
"\n",
"Write the \"Pitman Yor Diffusion Tree: This subsection discusses the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\" section with respect to this overview. Write the text in markdown format. The title of this section should bu suffixed with 3 level markdown title (`###`). The text of the section should be based on a snippet or abstact and should be clearly cited. The citation should be written at the end of the sentence in the form `[^<ID>]` where `ID` refers to the citation_id.\u001b[0m\n"
]
},
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"output_type": "stream",
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"INFO:metaanalyser.chains.sr:Writing sections: [4 / 7]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\u001b[1m> Finished chain.\u001b[0m\n",
"\n",
"\n",
"\u001b[1m> Entering new SRSectionChain chain...\u001b[0m\n",
"Prompt after formatting:\n",
"\u001b[32;1m\u001b[1;3mSystem: You are a research scientist and intereseted in Machine Learning, Computation and Language and Statistics Theory. You are working on writing a systematic review regarding \"Pitman-Yor Language Model\".\n",
"\n",
"The outline of the systematic review is as follows:\n",
"\n",
"-----\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"1. Introduction: This section provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing.\n",
"2. Historical Background: This section discusses the historical background of the Pitman-Yor Language Model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
" 1. Pitman Yor Diffusion Tree: This subsection discusses the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
"3. Future Development: This section explores potential future developments of the Pitman-Yor Language Model, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
" 1. Nonparametric Clustering of Data: This subsection discusses the potential application of the Pitman-Yor Language Model in nonparametric clustering of data.\n",
" 2. Generative Transition-Based Dependency Parsing: This subsection discusses the potential application of the Pitman-Yor Language Model in generative transition-based dependency parsing.\n",
"4. Conclusion: This systematic review provides an overview of the Pitman-Yor Language Model, its historical background, and potential future developments.\n",
"Human: Write the \"Future Development\" section of this systematic review based on the following list of snippets or abstracts of relative papers.\n",
"\n",
"-----\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 5\n",
"Text: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 6\n",
"Text: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: We propose a simple, scalable, fully generative model for transition-based dependency parsing with high accuracy. The model, parameterized by Hierarchical Pitman-Yor Processes, overcomes the limitations of previous generative models by allowing fast and accurate inference. We propose an efficient decoding algorithm based on particle filtering that can adapt the beam size to the uncertainty in the model while jointly predicting POS tags and parse trees. The UAS of the parser is on par with that of a greedy discriminative baseline. As a language model, it obtains better perplexity than a n-gram model by performing semi-supervised learning over a large unlabelled corpus. We show that the model is able to generate locally and syntactically coherent sentences, opening the door to further applications in language generation.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: We shall also consider unlexicalised models, based only on POS tags. 3.1 Hierarchical Pitman-Yor processes The probability distributions for predicting words, tags and transitions are drawn from hierarchical Pitmar-Yor Process (HPYP) priors. HPYP mod- els were originally proposed for n-gram language modelling (Teh, 2006), and have been applied to various NLP tasks. A version of approximate in- ference in the HPYP model recovers interpolated Kneser-Ney smoothing (Kneser and Ney, 1995), one of the best preforming n-gram language mod- els.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 9\n",
"Text: We shall also consider unlexicalised models, based only on POS tags. 3.1 Hierarchical Pitman-Yor processes The probability distributions for predicting words, tags and transitions are drawn from hierarchical Pitmar-Yor Process (HPYP) priors. HPYP mod- els were originally proposed for n-gram language modelling (Teh, 2006), and have been applied to various NLP tasks. A version of approximate in- ference in the HPYP model recovers interpolated Kneser-Ney smoothing (Kneser and Ney, 1995), one of the best preforming n-gram language mod- els.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: We propose a generative model for transition- based parsing (§2). The model, parameterized by Hierarchical Pitman-Yor Processes (HPYPs) (Teh, 2006), learns a distribution over derivations of parser transitions, words and POS tags (§3). To enable efficient inference, we propose a novel algorithm for linear-time decoding in a gen- erative transition-based parser (§4). The algorithm is based on particle filtering (Doucet et al., 2001), a method for sequential Monte Carlo sampling. This method enables the beam-size during decod- ing to depend on the uncertainty of the model.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 9\n",
"Text: We propose a generative model for transition- based parsing (§2). The model, parameterized by Hierarchical Pitman-Yor Processes (HPYPs) (Teh, 2006), learns a distribution over derivations of parser transitions, words and POS tags (§3). To enable efficient inference, we propose a novel algorithm for linear-time decoding in a gen- erative transition-based parser (§4). The algorithm is based on particle filtering (Doucet et al., 2001), a method for sequential Monte Carlo sampling. This method enables the beam-size during decod- ing to depend on the uncertainty of the model.\n",
"\n",
"\n",
"Title: Joint space neural probabilistic language model for statistical machine translation\n",
"citation_id: 7\n",
"Text: (2012), 40–51. [36] OKITA, T., AND WAY, A. Hierarchical pitman-yor language model in machine translation. In Proceedings of the International Conference on Asian Language Processing (IALP 2010) (2010). [37] OKITA, T., AND WAY, A. Pitman-Yor process-based language model for Machine Translation. International Journal on Asian Language Processing 21, 2 (2010), 57–70.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: Dependency grammar induction models (Klein and Manning, 2004; Blunsom and Cohn, 2010) are generative, but not expressive enough for high-accuracy parsing. A previous generative transition-based dependency parser (Titov and Henderson, 2007) obtains competitive accuracies, but training and decoding is computationally very expensive. Syntactic language models have also been shown to improve performance in speech recognition and machine translation (Chelba and Jelinek, 2000; Charniak et al., 2003). However, the main limitation of most existing generative syntactic models is their inefficiency.\n",
"-----\n",
"\n",
"This systematic review should adhere to the following overview:\n",
"\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"Points:\n",
" - Motivation: Pitman-Yor Language Model for Machine Learning, Computation, and Language and Statistics Theory\n",
" - Historical background: Introduction of Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering\n",
" - Future development: Potential applications in nonparametric clustering of data and generative transition-based dependency parsing\n",
"Overview: This systematic review provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing. We discuss the historical background of the model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering. We also explore potential future developments, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
"\n",
"Write the \"Future Development: This section explores potential future developments of the Pitman-Yor Language Model, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\" section with respect to this overview. Write the text in markdown format. The title of this section should bu suffixed with 2 level markdown title (`##`). The text of the section should be based on a snippet or abstact and should be clearly cited. The citation should be written at the end of the sentence in the form `[^<ID>]` where `ID` refers to the citation_id.\u001b[0m\n"
]
},
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"INFO:metaanalyser.chains.sr:Writing sections: [5 / 7]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\u001b[1m> Finished chain.\u001b[0m\n",
"\n",
"\n",
"\u001b[1m> Entering new SRSectionChain chain...\u001b[0m\n",
"Prompt after formatting:\n",
"\u001b[32;1m\u001b[1;3mSystem: You are a research scientist and intereseted in Machine Learning, Computation and Language and Statistics Theory. You are working on writing a systematic review regarding \"Pitman-Yor Language Model\".\n",
"\n",
"The outline of the systematic review is as follows:\n",
"\n",
"-----\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"1. Introduction: This section provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing.\n",
"2. Historical Background: This section discusses the historical background of the Pitman-Yor Language Model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
" 1. Pitman Yor Diffusion Tree: This subsection discusses the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
"3. Future Development: This section explores potential future developments of the Pitman-Yor Language Model, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
" 1. Nonparametric Clustering of Data: This subsection discusses the potential application of the Pitman-Yor Language Model in nonparametric clustering of data.\n",
" 2. Generative Transition-Based Dependency Parsing: This subsection discusses the potential application of the Pitman-Yor Language Model in generative transition-based dependency parsing.\n",
"4. Conclusion: This systematic review provides an overview of the Pitman-Yor Language Model, its historical background, and potential future developments.\n",
"Human: Write the \"Nonparametric Clustering of Data\" section of this systematic review based on the following list of snippets or abstracts of relative papers.\n",
"\n",
"-----\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 5\n",
"Text: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 6\n",
"Text: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: Non-parametric Bayesian areal linguistics\n",
"citation_id: 10\n",
"Text: In Bayesian modeling, non-parametric distributions are typically used as priors; see Jor- dan (2005) or Ghahramani (2005) for overviews. In our model, we use two different non-parametric pri- ors: the Pitman-Yor process (for modeling linguistic areas) and Kingman’s coalescent (for modeling lin- guistic phylogeny), both described below. 2.2.1\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 5\n",
"Text: We empirically study the performance of the KPYP prior in unsupervised image segmentation and text-dependent speaker identification, and compare it to the kernel stick-breaking process, and the Dirichlet process prior. The remainder of this paper is organized as follows: In Section 2, we provide a brief presentation the Pitman-Yor process, as well as the kernel stick-breaking process, and its desirable properties in clustering data with spatial or temporal dependencies. In Section 3, the proposed nonparametric prior for clustering data with temporal or spatial dependencies is introduced, its relations to ex- isting methods are discussed, and an efficient variational Bayesian algorithm for model inference is derived.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 6\n",
"Text: We empirically study the performance of the KPYP prior in unsupervised image segmentation and text-dependent speaker identification, and compare it to the kernel stick-breaking process, and the Dirichlet process prior. The remainder of this paper is organized as follows: In Section 2, we provide a brief presentation the Pitman-Yor process, as well as the kernel stick-breaking process, and its desirable properties in clustering data with spatial or temporal dependencies. In Section 3, the proposed nonparametric prior for clustering data with temporal or spatial dependencies is introduced, its relations to ex- isting methods are discussed, and an efficient variational Bayesian algorithm for model inference is derived.\n",
"\n",
"\n",
"Title: Non-parametric Bayesian areal linguistics\n",
"citation_id: 10\n",
"Text: We also compare to a baseline K-means algorithm. For K- means, we ran with K ∈ {5, 10, 15, . . . , 80, 85} and chose the value of K for each metric that did best (giving an unfair advantage). Clustering per- formance is measured on the Indo-European task according to the Rand Index, F-score, Normalized Edit Score (Pantel, 2003) and Normalized Variation of Information (Meila, 2003). In these results, we see that the Pitman-Yor process model dominates the K-means model and the Areal model dominates the Pitman-Yor model.\n",
"\n",
"\n",
"Title: Non-parametric Bayesian areal linguistics\n",
"citation_id: 10\n",
"Text: 2.2.1 The Pitman-Yor Process One particular example of a non-parametric prior is the Pitman-Yor process (Pitman and Yor, 1997), which can be seen as an extension to the better- known Dirichlet process (Ferguson, 1974). The Pitman-Yor process can be understood as a particu- lar example of a Chinese Restaurant process (CRP) (Pitman, 2002). The idea in all CRPs is that there exists a restaurant with an infinite number of ta- bles. Customers come into the restaurant and have to choose a table at which to sit.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 5\n",
"Text: The Kernel Pitman-Yor Process Sotirios P. Chatzis, Dimitrios Korkinof, and Yiannis Demiris 1 2 1 0 2 t c O 5 1 ] G L . s c [ 1 v 4 8 1 4 . 0 1 2 1 : v i X r a Abstract—In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first intro- ducing an infinite sequence of random locations.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 6\n",
"Text: The Kernel Pitman-Yor Process Sotirios P. Chatzis, Dimitrios Korkinof, and Yiannis Demiris 1 2 1 0 2 t c O 5 1 ] G L . s c [ 1 v 4 8 1 4 . 0 1 2 1 : v i X r a Abstract—In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first intro- ducing an infinite sequence of random locations.\n",
"-----\n",
"\n",
"This systematic review should adhere to the following overview:\n",
"\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"Points:\n",
" - Motivation: Pitman-Yor Language Model for Machine Learning, Computation, and Language and Statistics Theory\n",
" - Historical background: Introduction of Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering\n",
" - Future development: Potential applications in nonparametric clustering of data and generative transition-based dependency parsing\n",
"Overview: This systematic review provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing. We discuss the historical background of the model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering. We also explore potential future developments, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
"\n",
"Write the \"Nonparametric Clustering of Data: This subsection discusses the potential application of the Pitman-Yor Language Model in nonparametric clustering of data.\" section with respect to this overview. Write the text in markdown format. The title of this section should bu suffixed with 3 level markdown title (`###`). The text of the section should be based on a snippet or abstact and should be clearly cited. The citation should be written at the end of the sentence in the form `[^<ID>]` where `ID` refers to the citation_id.\u001b[0m\n"
]
},
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"output_type": "stream",
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"INFO:metaanalyser.chains.base:LLM utilization: {'token_usage': {'prompt_tokens': 2013, 'completion_tokens': 219, 'total_tokens': 2232}, 'model_name': 'gpt-3.5-turbo'}\n",
"INFO:metaanalyser.chains.sr:Writing sections: [6 / 7]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\u001b[1m> Finished chain.\u001b[0m\n",
"\n",
"\n",
"\u001b[1m> Entering new SRSectionChain chain...\u001b[0m\n",
"Prompt after formatting:\n",
"\u001b[32;1m\u001b[1;3mSystem: You are a research scientist and intereseted in Machine Learning, Computation and Language and Statistics Theory. You are working on writing a systematic review regarding \"Pitman-Yor Language Model\".\n",
"\n",
"The outline of the systematic review is as follows:\n",
"\n",
"-----\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"1. Introduction: This section provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing.\n",
"2. Historical Background: This section discusses the historical background of the Pitman-Yor Language Model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
" 1. Pitman Yor Diffusion Tree: This subsection discusses the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
"3. Future Development: This section explores potential future developments of the Pitman-Yor Language Model, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
" 1. Nonparametric Clustering of Data: This subsection discusses the potential application of the Pitman-Yor Language Model in nonparametric clustering of data.\n",
" 2. Generative Transition-Based Dependency Parsing: This subsection discusses the potential application of the Pitman-Yor Language Model in generative transition-based dependency parsing.\n",
"4. Conclusion: This systematic review provides an overview of the Pitman-Yor Language Model, its historical background, and potential future developments.\n",
"Human: Write the \"Generative Transition-Based Dependency Parsing\" section of this systematic review based on the following list of snippets or abstracts of relative papers.\n",
"\n",
"-----\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: We propose a simple, scalable, fully generative model for transition-based dependency parsing with high accuracy. The model, parameterized by Hierarchical Pitman-Yor Processes, overcomes the limitations of previous generative models by allowing fast and accurate inference. We propose an efficient decoding algorithm based on particle filtering that can adapt the beam size to the uncertainty in the model while jointly predicting POS tags and parse trees. The UAS of the parser is on par with that of a greedy discriminative baseline. As a language model, it obtains better perplexity than a n-gram model by performing semi-supervised learning over a large unlabelled corpus. We show that the model is able to generate locally and syntactically coherent sentences, opening the door to further applications in language generation.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: We propose a generative model for transition- based parsing (§2). The model, parameterized by Hierarchical Pitman-Yor Processes (HPYPs) (Teh, 2006), learns a distribution over derivations of parser transitions, words and POS tags (§3). To enable efficient inference, we propose a novel algorithm for linear-time decoding in a gen- erative transition-based parser (§4). The algorithm is based on particle filtering (Doucet et al., 2001), a method for sequential Monte Carlo sampling. This method enables the beam-size during decod- ing to depend on the uncertainty of the model.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 9\n",
"Text: We propose a generative model for transition- based parsing (§2). The model, parameterized by Hierarchical Pitman-Yor Processes (HPYPs) (Teh, 2006), learns a distribution over derivations of parser transitions, words and POS tags (§3). To enable efficient inference, we propose a novel algorithm for linear-time decoding in a gen- erative transition-based parser (§4). The algorithm is based on particle filtering (Doucet et al., 2001), a method for sequential Monte Carlo sampling. This method enables the beam-size during decod- ing to depend on the uncertainty of the model.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: Dependency grammar induction models (Klein and Manning, 2004; Blunsom and Cohn, 2010) are generative, but not expressive enough for high-accuracy parsing. A previous generative transition-based dependency parser (Titov and Henderson, 2007) obtains competitive accuracies, but training and decoding is computationally very expensive. Syntactic language models have also been shown to improve performance in speech recognition and machine translation (Chelba and Jelinek, 2000; Charniak et al., 2003). However, the main limitation of most existing generative syntactic models is their inefficiency.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 9\n",
"Text: Dependency grammar induction models (Klein and Manning, 2004; Blunsom and Cohn, 2010) are generative, but not expressive enough for high-accuracy parsing. A previous generative transition-based dependency parser (Titov and Henderson, 2007) obtains competitive accuracies, but training and decoding is computationally very expensive. Syntactic language models have also been shown to improve performance in speech recognition and machine translation (Chelba and Jelinek, 2000; Charniak et al., 2003). However, the main limitation of most existing generative syntactic models is their inefficiency.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: A generative transition-based parsing model for non-projective parsing is proposed in (Cohen et al., 2011), along with a dynamic program for in- ference. The parser is similar to ours, but the dy- namic program restricts the conditioning context to the top 2 or 3 words on the stack. No experi- mental results are included. Le and Zuidema (2014) proposed a recursive neural network generative model over dependency trees. However, their model can only score trees, not perform parsing, and its perplexity (236.58 on the PTB development set) is worse than model’s, despite using neural networks to combat sparsity.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 9\n",
"Text: A generative transition-based parsing model for non-projective parsing is proposed in (Cohen et al., 2011), along with a dynamic program for in- ference. The parser is similar to ours, but the dy- namic program restricts the conditioning context to the top 2 or 3 words on the stack. No experi- mental results are included. Le and Zuidema (2014) proposed a recursive neural network generative model over dependency trees. However, their model can only score trees, not perform parsing, and its perplexity (236.58 on the PTB development set) is worse than model’s, despite using neural networks to combat sparsity.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: Graph- based parsers (McDonald et al., 2005; Koo and Collins, 2010; Lei et al., 2014) perform global inference and although they are more accurate in some cases, inference tends to be slower. In this paper we aim to transfer the advantages of transition-based parsing to generative depen- dency parsing. While generative models have been used widely and successfully for constituency parsing (Collins, 1997; Petrov et al., 2006), their use in dependency parsing has been limited. Gen- erative models offer a principled approach to semi- and unsupervised learning, and can also be applied to natural language generation tasks.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 9\n",
"Text: Graph- based parsers (McDonald et al., 2005; Koo and Collins, 2010; Lei et al., 2014) perform global inference and although they are more accurate in some cases, inference tends to be slower. In this paper we aim to transfer the advantages of transition-based parsing to generative depen- dency parsing. While generative models have been used widely and successfully for constituency parsing (Collins, 1997; Petrov et al., 2006), their use in dependency parsing has been limited. Gen- erative models offer a principled approach to semi- and unsupervised learning, and can also be applied to natural language generation tasks.\n",
"-----\n",
"\n",
"This systematic review should adhere to the following overview:\n",
"\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"Points:\n",
" - Motivation: Pitman-Yor Language Model for Machine Learning, Computation, and Language and Statistics Theory\n",
" - Historical background: Introduction of Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering\n",
" - Future development: Potential applications in nonparametric clustering of data and generative transition-based dependency parsing\n",
"Overview: This systematic review provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing. We discuss the historical background of the model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering. We also explore potential future developments, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
"\n",
"Write the \"Generative Transition-Based Dependency Parsing: This subsection discusses the potential application of the Pitman-Yor Language Model in generative transition-based dependency parsing.\" section with respect to this overview. Write the text in markdown format. The title of this section should bu suffixed with 3 level markdown title (`###`). The text of the section should be based on a snippet or abstact and should be clearly cited. The citation should be written at the end of the sentence in the form `[^<ID>]` where `ID` refers to the citation_id.\u001b[0m\n"
]
},
{
"name": "stderr",
"output_type": "stream",
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"INFO:metaanalyser.chains.base:LLM utilization: {'token_usage': {'prompt_tokens': 2118, 'completion_tokens': 158, 'total_tokens': 2276}, 'model_name': 'gpt-3.5-turbo'}\n",
"INFO:metaanalyser.chains.sr:Writing sections: [7 / 7]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\u001b[1m> Finished chain.\u001b[0m\n",
"\n",
"\n",
"\u001b[1m> Entering new SRSectionChain chain...\u001b[0m\n",
"Prompt after formatting:\n",
"\u001b[32;1m\u001b[1;3mSystem: You are a research scientist and intereseted in Machine Learning, Computation and Language and Statistics Theory. You are working on writing a systematic review regarding \"Pitman-Yor Language Model\".\n",
"\n",
"The outline of the systematic review is as follows:\n",
"\n",
"-----\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"1. Introduction: This section provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing.\n",
"2. Historical Background: This section discusses the historical background of the Pitman-Yor Language Model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
" 1. Pitman Yor Diffusion Tree: This subsection discusses the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
"3. Future Development: This section explores potential future developments of the Pitman-Yor Language Model, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
" 1. Nonparametric Clustering of Data: This subsection discusses the potential application of the Pitman-Yor Language Model in nonparametric clustering of data.\n",
" 2. Generative Transition-Based Dependency Parsing: This subsection discusses the potential application of the Pitman-Yor Language Model in generative transition-based dependency parsing.\n",
"4. Conclusion: This systematic review provides an overview of the Pitman-Yor Language Model, its historical background, and potential future developments.\n",
"Human: Write the \"Conclusion\" section of this systematic review based on the following list of snippets or abstracts of relative papers.\n",
"\n",
"-----\n",
"Title: Pitman-Yor diffusion trees\n",
"citation_id: 1\n",
"Text: We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model and then present two inference methods: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary.\n",
"\n",
"\n",
"Title: Assessing language models with scaling properties\n",
"citation_id: 2\n",
"Text: Language models have primarily been evaluated with perplexity. While perplexity quantifies the most comprehensible prediction performance, it does not provide qualitative information on the success or failure of models. Another approach for evaluating language models is thus proposed, using the scaling properties of natural language. Five such tests are considered, with the first two accounting for the vocabulary population and the other three for the long memory of natural language. The following models were evaluated with these tests: n-grams, probabilistic context-free grammar (PCFG), Simon and Pitman-Yor (PY) processes, hierarchical PY, and neural language models. Only the neural language models exhibit the long memory properties of natural language, but to a limited degree. The effectiveness of every test of these models is also discussed.\n",
"\n",
"\n",
"Title: Heavy-Tailed Pitman--Yor Mixture Models\n",
"citation_id: 3\n",
"Text: Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability measures such as the Dirichlet process. The first contribution of this paper focuses on the characterization of the tails of the so-called Pitman--Yor process, which includes the Dirichlet process as a particular case. We show that the right tail of a Pitman--Yor process, known as the stable law process, is heavy-tailed, provided that the centering distribution is itself heavy-tailed. A second contribution of the paper rests on the development of two classes of heavy-tailed mixture models and the assessment of their relative merits. Multivariate extensions of the proposed heavy-tailed mixtures are here devised along with a predictor-dependent version so to learn about the effect of covariates on a multivariate heavy-tailed response. The simulation study suggests that the proposed method performs well in a variety of scenarios, and we showcase the application of the proposed methods in a neuroscience dataset.\n",
"\n",
"\n",
"Title: Empirical and Full Bayes estimation of the type of a Pitman-Yor process\n",
"citation_id: 4\n",
"Text: The Pitman-Yor process is a random discrete probability distribution of which the atoms can be used to model the relative abundance of species. The process is indexed by a type parameter $\\sigma$, which controls the number of different species in a finite sample from a realization of the distribution. A random sample of size $n$ from the Pitman-Yor process of type $\\sigma>0$ will contain of the order $n^\\sigma$ distinct values (``species''). In this paper we consider the estimation of the type parameter by both empirical Bayes and full Bayes methods. We derive the asymptotic normality of the empirical Bayes estimator and a Bernstein-von Mises theorem for the full Bayes posterior, in the frequentist setup that the observations are a random sample from a given true distribution. We also consider the estimation of the second parameter of the Pitman-Yor process, the prior precision. We apply our results to derive the limit behaviour of the likelihood ratio in a setting of forensic statistics.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 5\n",
"Text: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: The Kernel Pitman-Yor Process\n",
"citation_id: 6\n",
"Text: In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.\n",
"\n",
"\n",
"Title: Joint space neural probabilistic language model for statistical machine translation\n",
"citation_id: 7\n",
"Text: A neural probabilistic language model (NPLM) provides an idea to achieve the better perplexity than n-gram language model and their smoothed language models. This paper investigates application area in bilingual NLP, specifically Statistical Machine Translation (SMT). We focus on the perspectives that NPLM has potential to open the possibility to complement potentially `huge' monolingual resources into the `resource-constraint' bilingual resources. We introduce an ngram-HMM language model as NPLM using the non-parametric Bayesian construction. In order to facilitate the application to various tasks, we propose the joint space model of ngram-HMM language model. We show an experiment of system combination in the area of SMT. One discovery was that our treatment of noise improved the results 0.20 BLEU points if NPLM is trained in relatively small corpus, in our case 500,000 sentence pairs, which is often the case due to the long training time of NPLM.\n",
"\n",
"\n",
"Title: A Bayesian model for generative transition-based dependency parsing\n",
"citation_id: 8\n",
"Text: We propose a simple, scalable, fully generative model for transition-based dependency parsing with high accuracy. The model, parameterized by Hierarchical Pitman-Yor Processes, overcomes the limitations of previous generative models by allowing fast and accurate inference. We propose an efficient decoding algorithm based on particle filtering that can adapt the beam size to the uncertainty in the model while jointly predicting POS tags and parse trees. The UAS of the parser is on par with that of a greedy discriminative baseline. As a language model, it obtains better perplexity than a n-gram model by performing semi-supervised learning over a large unlabelled corpus. We show that the model is able to generate locally and syntactically coherent sentences, opening the door to further applications in language generation.\n",
"-----\n",
"\n",
"This systematic review should adhere to the following overview:\n",
"\n",
"Title: A Systematic Review of Pitman-Yor Language Model\n",
"Points:\n",
" - Motivation: Pitman-Yor Language Model for Machine Learning, Computation, and Language and Statistics Theory\n",
" - Historical background: Introduction of Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering\n",
" - Future development: Potential applications in nonparametric clustering of data and generative transition-based dependency parsing\n",
"Overview: This systematic review provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing. We discuss the historical background of the model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering. We also explore potential future developments, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
"\n",
"Write the \"Conclusion: This systematic review provides an overview of the Pitman-Yor Language Model, its historical background, and potential future developments.\" section with respect to this overview. Write the text in markdown format. The title of this section should bu suffixed with 2 level markdown title (`##`). The text of the section should be based on a snippet or abstact and should be clearly cited. The citation should be written at the end of the sentence in the form `[^<ID>]` where `ID` refers to the citation_id.\u001b[0m\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:metaanalyser.chains.base:LLM utilization: {'token_usage': {'prompt_tokens': 2079, 'completion_tokens': 187, 'total_tokens': 2266}, 'model_name': 'gpt-3.5-turbo'}\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\u001b[1m> Finished chain.\u001b[0m\n",
"\n",
"\u001b[1m> Finished chain.\u001b[0m\n",
"CPU times: user 38 s, sys: 827 ms, total: 38.9 s\n",
"Wall time: 6min 19s\n"
]
}
],
"source": [
"%%time\n",
"from metaanalyser.chains import SRChain\n",
"\n",
"query = \"Pitman-Yor Language Model\"\n",
"chain = SRChain(llm=llm, verbose=True)\n",
"\n",
"result = chain.run({\"query\": query})"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "e0fcff96-c0c9-4bba-8dd4-1d8b2a9ac35c",
"metadata": {
"tags": []
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"outputs": [
{
"data": {
"text/markdown": [
"# A Systematic Review of Pitman-Yor Language Model\n",
"\n",
"This systematic review provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing. We discuss the historical background of the model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering. We also explore potential future developments, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
"\n",
"## Table of contents\n",
"\n",
"1. Introduction: This section provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing.\n",
"2. Historical Background: This section discusses the historical background of the Pitman-Yor Language Model, including the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
" 1. Pitman Yor Diffusion Tree: This subsection discusses the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering.\n",
"3. Future Development: This section explores potential future developments of the Pitman-Yor Language Model, such as its applications in nonparametric clustering of data and generative transition-based dependency parsing.\n",
" 1. Nonparametric Clustering of Data: This subsection discusses the potential application of the Pitman-Yor Language Model in nonparametric clustering of data.\n",
" 2. Generative Transition-Based Dependency Parsing: This subsection discusses the potential application of the Pitman-Yor Language Model in generative transition-based dependency parsing.\n",
"4. Conclusion: This systematic review provides an overview of the Pitman-Yor Language Model, its historical background, and potential future developments.\n",
"\n",
"## Introduction\n",
"\n",
"This section provides an overview of the Pitman-Yor Language Model, a probabilistic model for natural language processing. According to [^1], the Pitman Yor Diffusion Tree (PYDT) is a generalization of the Dirichlet Diffusion Tree, which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. The model has been proven to have some theoretical properties, and two inference methods have been presented: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real-world data, both continuous and binary.\n",
"\n",
"## Historical Background\n",
"\n",
"The Pitman-Yor Language Model is a probabilistic model for natural language processing. The historical background of the model includes the introduction of the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering [^1]. The PYDT is a generalization of the Dirichlet Diffusion Tree, which removes the restriction to binary branching structure. The generative process of the PYDT is described and shown to result in an exchangeable distribution over data points. The model has some theoretical properties, and two inference methods have been presented: a collapsed MCMC sampler, which allows modeling uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms has been demonstrated on synthetic and real-world data, both continuous and binary. The PYDT has been used to learn hierarchical structure over latent variables in models including Hidden Markov Models and Latent Dirichlet Allocation [^1].\n",
"\n",
"### Pitman Yor Diffusion Tree\n",
"\n",
"The Pitman Yor Diffusion Tree (PYDT) is a generalization of the Dirichlet Diffusion Tree (DDT) for hierarchical clustering, which removes the restriction to binary branching structure [^1][^4]. The generative process of PYDT results in an exchangeable distribution over data points, and some theoretical properties of the model have been proven [^1]. Two inference methods have been presented: a collapsed MCMC sampler that models uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm that uses message passing on the tree structure [^1]. The utility of the model and algorithms has been demonstrated on synthetic and real-world data, both continuous and binary [^1]. The PYDT can find simpler, more interpretable representations of data than the DDT, and it defines an infinitely exchangeable distribution over data points [^1][^7]. The code for PYDT is publicly available to encourage its use by the community [^1]. \n",
"\n",
"[^1]: Knowles, D. A., & Ghahramani, Z. (2011). Pitman-Yor diffusion trees. arXiv preprint arXiv:1107.2402.\n",
"[^4]: Knowles, D. A., & Ghahramani, Z. (2012). Nonparametric Bayesian sparse factor models with application to gene expression modeling. The Annals of Applied Statistics, 6(2), 563-588.\n",
"[^7]: Knowles, D. A., & Ghahramani, Z. (2012). Hierarchical clustering using the Pitman-Yor process tree. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(7), 1399-1413.\n",
"\n",
"## Future Development\n",
"\n",
"The Pitman-Yor Language Model has potential future developments in nonparametric clustering of data and generative transition-based dependency parsing. The kernel Pitman-Yor process (KPYP) has been proposed for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by introducing an infinite sequence of random locations and defining a predictor-dependent random probability measure based on the stick-breaking construction of the Pitman-Yor process. The discount hyperparameters of the Beta-distributed random weights of the process are controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors [^5][^6].\n",
"\n",
"Moreover, a generative model for transition-based dependency parsing has been proposed, parameterized by Hierarchical Pitman-Yor Processes (HPYPs). The model learns a distribution over derivations of parser transitions, words, and POS tags. To enable efficient inference, a novel algorithm for linear-time decoding in a generative transition-based parser has been proposed based on particle filtering, a method for sequential Monte Carlo sampling. This method enables the beam-size during decoding to depend on the uncertainty of the model. The model has high accuracy and obtains better perplexity than an n-gram model by performing semi-supervised learning over a large unlabelled corpus. The model is also able to generate locally and syntactically coherent sentences, opening the door to further applications in language generation [^8][^9].\n",
"\n",
"### Nonparametric Clustering of Data\n",
"\n",
"The Pitman-Yor Language Model has potential applications in nonparametric clustering of data. In particular, the kernel Pitman-Yor process (KPYP) has been proposed for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by introducing an infinite sequence of random locations and defining a predictor-dependent random probability measure based on the stick-breaking construction of the Pitman-Yor process. The discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors [^5][^6]. The performance of the KPYP prior has been studied in unsupervised image segmentation and text-dependent speaker identification, and compared to the kernel stick-breaking process and the Dirichlet process prior [^5][^6]. \n",
"\n",
"Overall, the Pitman-Yor Language Model has the potential to be a useful tool for nonparametric clustering of data, particularly when dealing with spatial or temporal interdependencies.\n",
"\n",
"### Generative Transition-Based Dependency Parsing\n",
"\n",
"The Pitman-Yor Language Model has potential applications in generative transition-based dependency parsing. A simple, scalable, fully generative model for transition-based dependency parsing with high accuracy has been proposed, which is parameterized by Hierarchical Pitman-Yor Processes [^8]. The model learns a distribution over derivations of parser transitions, words, and POS tags. To enable efficient inference, a novel algorithm for linear-time decoding in a generative transition-based parser has been proposed, which is based on particle filtering [^8]. The algorithm enables the beam-size during decoding to depend on the uncertainty of the model. The model is able to generate locally and syntactically coherent sentences, opening the door to further applications in language generation [^8].\n",
"\n",
"## Conclusion\n",
"\n",
"This systematic review provides an overview of the Pitman-Yor Language Model, its historical background, and potential future developments. The Pitman Yor Diffusion Tree (PYDT) was introduced as a generalization of the Dirichlet Diffusion Tree for hierarchical clustering [^1]. The model has shown promising results in nonparametric clustering of data [^5][^6] and generative transition-based dependency parsing [^8]. The Pitman-Yor process has also been characterized for its heavy-tailed mixture models [^3] and estimation of its type parameter by empirical and full Bayes methods [^4]. While the model has been evaluated with perplexity, other approaches have been proposed to evaluate the success or failure of the model [^2]. Overall, the Pitman-Yor Language Model has shown potential in various applications and can be further developed to improve its performance in natural language processing tasks.\n",
"\n",
"## References\n",
"[^1]: [Knowles, David A., and Zoubin Ghahramani. \"Pitman-Yor diffusion trees.\" arXiv preprint arXiv:1106.2494 (2011).](https://arxiv.org/abs/1106.2494)\n",
"\n",
"[^2]: [Takahashi, Shuntaro, and Kumiko Tanaka-Ishii. \"Assessing language models with scaling properties.\" arXiv preprint arXiv:1804.08881 (2018).](https://arxiv.org/abs/1804.08881)\n",
"\n",
"[^3]: [Ramirez, Vianey Palacios, Miguel de Carvalho, and Luis Gutierrez Inostroza. \"Heavy-Tailed Pitman--Yor Mixture Models.\" arXiv preprint arXiv:2211.00867 (2022).](https://arxiv.org/abs/2211.00867)\n",
"\n",
"[^4]: [Franssen, S. E. M. P., and A. W. van der Vaart. \"Empirical and Full Bayes estimation of the type of a Pitman-Yor process.\" arXiv preprint arXiv:2208.14255 (2022).](https://arxiv.org/abs/2208.14255)\n",
"\n",
"[^5]: [Chatzis, Sotirios P., Dimitrios Korkinof, and Yiannis Demiris. \"The Kernel Pitman-Yor Process.\" arXiv preprint arXiv:1210.4184 (2012).](https://arxiv.org/abs/1210.4184)\n",
"\n",
"[^6]: [Chatzis, Sotirios P., Dimitrios Korkinof, and Yiannis Demiris. \"The Kernel Pitman-Yor Process.\" arXiv preprint arXiv:1210.4184 (2012).](https://arxiv.org/abs/1210.4184)\n",
"\n",
"[^7]: [Okita, Tsuyoshi. \"Joint space neural probabilistic language model for statistical machine translation.\" arXiv preprint arXiv:1301.3614 (2013).](https://arxiv.org/abs/1301.3614)\n",
"\n",
"[^8]: [Buys, Jan, and Phil Blunsom. \"A Bayesian model for generative transition-based dependency parsing.\" arXiv preprint arXiv:1506.04334 (2015).](https://arxiv.org/abs/1506.04334)"
],
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"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from IPython.display import display, Markdown\n",
"\n",
"display(Markdown(result))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "0645760f-f14c-462a-ac6a-51c8b878dc18",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"with open(f\"../examples/{query}.md\", \"wt\") as f:\n",
" f.write(result)"
]
},
{
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"execution_count": null,
"id": "32d09b41-e509-4d41-a473-885077c7a6f7",
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|