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Which of the following is wrong regarding Ontologies? | Many of those who doubt the possibility of developing wide agreement on a common upper ontology fall into one of two traps: they assert that there is no possibility of universal agreement on any conceptual scheme; but they argue that a practical common ontology does not need to have universal agreement, it only needs a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is wrong regarding Ontologies? | Many of those who doubt the possibility of developing wide agreement on a common upper ontology fall into one of two traps: they assert that there is no possibility of universal agreement on any conceptual scheme; but they argue that a practical common ontology does not need to have universal agreement, it only needs a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following statements is correct concerning the use of Pearson’s Correlation for user- based collaborative filtering? | The collaborative filtering method: Collected user data may be assessed in aggregate (across multiple users) using machine learning techniques to cluster interaction patterns to user models and classify specific user patterns to such models. The website may then be adapted to target clusters of users. In this approach,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following statements is correct concerning the use of Pearson’s Correlation for user- based collaborative filtering? | These predictions are specific to the user, but use information gleaned from many users. This differs from the simpler approach of giving an average (non-specific) score for each item of interest, for example based on its number of votes. In the more general sense, collaborative filtering is the process of filtering fo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
After the join step, the number of k+1-itemsets | If the item is less than entry Fk−1, discard the elements from positions Fk−1 + 1 to n. Set k = k − 1 and return to step 2. If the item is greater than entry Fk−1, discard the elements from positions 1 to Fk−1. Renumber the remaining elements from 1 to Fk−2, set k = k − 2, and return to step 2.Alternative implementatio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
After the join step, the number of k+1-itemsets | The final list in this sequence, M k {\displaystyle M_{k}} , is equal to L k {\displaystyle L_{k}} ; each earlier list M i {\displaystyle M_{i}} is formed by merging L i {\displaystyle L_{i}} with every second item from M i + 1 {\displaystyle M_{i+1}} . With each item x {\displaystyle x} in this merged list, we store t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which is true about the use of entropy in decision tree induction? | Machine learning techniques arise largely from statistics and also information theory. In general, entropy is a measure of uncertainty and the objective of machine learning is to minimize uncertainty. Decision tree learning algorithms use relative entropy to determine the decision rules that govern the data at each nod... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which is true about the use of entropy in decision tree induction? | J.R. Quinlan (1986). "Induction of Decision Trees". Machine Learning. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement User-based collaborative filtering using the following formula: \begin{equation} {r}_{x}(a) = \bar{r}_{x} + \frac{\sum\limits_{y \in N_{U}(x)} sim(x, y) (r_{y}(a) - \bar{r}_{y})}{\sum\limits_{y \in N_{U}(x)}|sim(x, y)|} \end{equation} You will create a function that takes as input the ratings and the simila... | Collaborative filtering systems have many forms, but many common systems can be reduced to two steps: Look for users who share the same rating patterns with the active user (the user whom the prediction is for). Use the ratings from those like-minded users found in step 1 to calculate a prediction for the active userTh... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement User-based collaborative filtering using the following formula: \begin{equation} {r}_{x}(a) = \bar{r}_{x} + \frac{\sum\limits_{y \in N_{U}(x)} sim(x, y) (r_{y}(a) - \bar{r}_{y})}{\sum\limits_{y \in N_{U}(x)}|sim(x, y)|} \end{equation} You will create a function that takes as input the ratings and the simila... | The authors provide three types of scores: Similar users: this score is proportional to the similarity in behavior of users for visiting places. Mathematically, the similarity score between two users is computed as follows:Where s ( u , i ) {\textstyle s(u,i)} denotes the probability of visiting place i {\textstyle i} ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which statement is false about clustering? | There is no objectively "correct" clustering algorithm, but as it was noted, "clustering is in the eye of the beholder." The most appropriate clustering algorithm for a particular problem often needs to be chosen experimentally, unless there is a mathematical reason to prefer one cluster model over another. An algorith... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which statement is false about clustering? | There is no objectively "correct" clustering algorithm, but as it was noted, "clustering is in the eye of the beholder." The most appropriate clustering algorithm for a particular problem often needs to be chosen experimentally, unless there is a mathematical reason to prefer one cluster model over another. An algorith... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Modularity clustering will end up always with the same community structure? | The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. Modularity is a scale value between −0.5 (non-modular clustering) and 1 (fully modular clustering) that measures the relative density of edges inside communities with respect to edges outside communitie... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Modularity clustering will end up always with the same community structure? | Biological networks, including animal brains, exhibit a high degree of modularity. However, modularity maximization is not statistically consistent, and finds communities in its own null model, i.e. fully random graphs, and therefore it cannot be used to find statistically significant community structures in empirical ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement weigthing estimation of kNN classification | In fault detection and diagnosis, mathematical classification models which in fact belong to supervised learning methods, are trained on the training set of a labeled dataset to accurately identify the redundancies, faults and anomalous samples. During the past decades, there are different classification and preprocess... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement weigthing estimation of kNN classification | The k-NN algorithm is a well known pattern recognition algorithm where a set of predetermined prototypes {pk} are used during the sample, or testing phase, of a supposed event. The prototypes model the events that are of interest in the application. The distance between each test vector and each prototype is calculated... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For his awesome research, Tugrulcan is going to use the Pagerank with teleportation and HITS algorithm, not on a network of webpages but on the retweet network of Twitter! The retweet network is a directed graph, where nodes are users and an edge going out from a user A and to a user B means that "User A retweeted User... | A Twitter bot is a computer program that can automatically tweet, retweet, and follow other accounts. Twitter's open application programming interface and the availability of cloud servers make it possible for Twitter bots to exist within the social networking site. Benign Twitter bots may generate creative content and... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For his awesome research, Tugrulcan is going to use the Pagerank with teleportation and HITS algorithm, not on a network of webpages but on the retweet network of Twitter! The retweet network is a directed graph, where nodes are users and an edge going out from a user A and to a user B means that "User A retweeted User... | It is sometimes desirable to identify when a Twitter account is controlled by a internet bot. Following a test period, Twitter rolled out labels to identify bot accounts and automated tweets in February 2022.Detecting non-human Twitter users has been of interest to academics.In a 2012 paper, Chu et al. propose the foll... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement kNN function (finding k nearest documents for a given document) | k-nearest neighbor (k-NN) query takes the cardinality of the input set as an input parameter. For a given query object Q ∈ D and an integer k ≥ 1, the k-NN query NN(Q, k) selects the k indexed objects which have the shortest distance from Q, according to the distance function d. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement kNN function (finding k nearest documents for a given document) | function knn_search is input: t, the target point for the query k, the number of nearest neighbors of t to search for Q, max-first priority queue containing at most k points B, a node, or ball, in the tree output: Q, containing the k nearest neighbors from within B if distance(t, B.pivot) - B.radius ≥ distance(t, Q.fir... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Following the notation used in class, let us denote the set of terms by $T=\{k_i|i=1,...,m\}$, the set of documents by $D=\{d_j |j=1,...,n\}$, and let $d_i=(w_{1j},w_{2j},...,w_{mj})$. We are also given a query $q=(w_{1q},w_{2q},...,w_{mq})$. In the lecture we studied that, $sim(q,d_j) = \sum^m_{i=1} \frac{w_{ij}}{|... | Similarities are computed as probabilities that a document is relevant for a given query. Probabilistic theorems like the Bayes' theorem are often used in these models. Binary Independence Model Probabilistic relevance model on which is based the okapi (BM25) relevance function Uncertain inference Language models Diver... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Following the notation used in class, let us denote the set of terms by $T=\{k_i|i=1,...,m\}$, the set of documents by $D=\{d_j |j=1,...,n\}$, and let $d_i=(w_{1j},w_{2j},...,w_{mj})$. We are also given a query $q=(w_{1q},w_{2q},...,w_{mq})$. In the lecture we studied that, $sim(q,d_j) = \sum^m_{i=1} \frac{w_{ij}}{|... | Zhao and Callan (2010) were perhaps the first to quantitatively study the vocabulary mismatch problem in a retrieval setting. Their results show that an average query term fails to appear in 30-40% of the documents that are relevant to the user query. They also showed that this probability of mismatch is a central prob... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement Latent Semantic Indexing by selecting the first x largest singular values of the term document matrix Hint 1: np.linalg.svd(M, full_matrices=False) performs SVD on the matrix $\mathbf{M}$ and returns $\mathbf{K}, \mathbf{S}, \mathbf{D}^T$ - $\mathbf{K}, \mathbf{D}^T$ are matrices with orthonormal column... | A rank-reduced, singular value decomposition is performed on the matrix to determine patterns in the relationships between the terms and concepts contained in the text. The SVD forms the foundation for LSI. It computes the term and document vector spaces by approximating the single term-frequency matrix, A {\displaysty... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement Latent Semantic Indexing by selecting the first x largest singular values of the term document matrix Hint 1: np.linalg.svd(M, full_matrices=False) performs SVD on the matrix $\mathbf{M}$ and returns $\mathbf{K}, \mathbf{S}, \mathbf{D}^T$ - $\mathbf{K}, \mathbf{D}^T$ are matrices with orthonormal column... | The computed Tk and Dk matrices define the term and document vector spaces, which with the computed singular values, Sk, embody the conceptual information derived from the document collection. The similarity of terms or documents within these spaces is a factor of how close they are to each other in these spaces, typic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
When searching for an entity 𝑒𝑛𝑒𝑤 that has a given relationship 𝑟 with a given entity 𝑒 | This is called reification of a relationship. Like any other entity, it must be an instance of an entity type. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
When searching for an entity 𝑒𝑛𝑒𝑤 that has a given relationship 𝑟 with a given entity 𝑒 | For example, “I’m looking for a male sister” refers to no actual entity. However, the ambiguity of its specificity (are you looking for a particular male sister, or any male sister?) is retained. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement the modularity metric for communities. | The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. Modularity is a scale value between −0.5 (non-modular clustering) and 1 (fully modular clustering) that measures the relative density of edges inside communities with respect to edges outside communitie... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement the modularity metric for communities. | Seed product to attract a community Multiple stakeholders for a variety of contributions Modularity to attract contributors and users | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following graph analysis techniques do you believe would be most appropriate to identify communities on a social graph? | The problem of detecting the community features is one of the main issues in the study of networking systems. Social networks naturally tend to divide themselves into communities or modules. However, some world networks are too big so they must be simplified before information can be extracted. As a result, an effectiv... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following graph analysis techniques do you believe would be most appropriate to identify communities on a social graph? | The evaluation of algorithms, to detect which are better at detecting community structure, is still an open question. It must be based on analyses of networks of known structure. A typical example is the "four groups" test, in which a network is divided into four equally-sized groups (usually of 32 nodes each) and the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following models for generating vector representations for text require to precompute the frequency of co-occurrence of words from the vocabulary in the document collection | Considering observations in the form of co-occurrences ( w , d ) {\displaystyle (w,d)} of words and documents, PLSA models the probability of each co-occurrence as a mixture of conditionally independent multinomial distributions: P ( w , d ) = ∑ c P ( c ) P ( d | c ) P ( w | c ) = P ( d ) ∑ c P ( c | d ) P ( w | c ) {\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following models for generating vector representations for text require to precompute the frequency of co-occurrence of words from the vocabulary in the document collection | Considering observations in the form of co-occurrences ( w , d ) {\displaystyle (w,d)} of words and documents, PLSA models the probability of each co-occurrence as a mixture of conditionally independent multinomial distributions: P ( w , d ) = ∑ c P ( c ) P ( d | c ) P ( w | c ) = P ( d ) ∑ c P ( c | d ) P ( w | c ) {\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For which document classifier the training cost is low and inference is expensive? | The authors note that using support vector machines (SVM) and hundreds of documents give inferior performance, but does not specify which features or documents the SVM was trained/tested on. A fair comparison would use the same features and document sets as those used by the manual threshold classifier. == References =... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For which document classifier the training cost is low and inference is expensive? | The textual data's ever-growing nature makes the task overwhelmingly difficult for the researchers to complete the task on time.Previously, the research mainly focused on document level classification. However, classifying a document level suffers less accuracy, as an article may have diverse types of expressions invol... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A word embedding for given corpus | In natural language processing (NLP), a word embedding is a representation of a word. The embedding is used in text analysis. Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that words that are closer in the vector space are expected to be similar in meaning. Wor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A word embedding for given corpus | Unsupervised word sense disambiguation rivaling supervised methods. In Proc. of the 33rd Annual Meeting of the Association for Computational Linguistics. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In Ranked Retrieval, the result at position k is non-relevant and at k+1 is relevant. Which of the following is always true?
Hint: P@k and R@k are the precision and recall of the result set consisting of the k top-ranked documents. | For modern (web-scale) information retrieval, recall is no longer a meaningful metric, as many queries have thousands of relevant documents, and few users will be interested in reading all of them. Precision at k documents (P@k) is still a useful metric (e.g., P@10 or "Precision at 10" corresponds to the number of rele... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In Ranked Retrieval, the result at position k is non-relevant and at k+1 is relevant. Which of the following is always true?
Hint: P@k and R@k are the precision and recall of the result set consisting of the k top-ranked documents. | For modern (web-scale) information retrieval, recall is no longer a meaningful metric, as many queries have thousands of relevant documents, and few users will be interested in reading all of them. Precision at k documents (P@k) is still a useful metric (e.g., P@10 or "Precision at 10" corresponds to the number of rele... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Regarding the Expectation-Maximization algorithm, which one of the following false? | Via a modification of an expectation-maximization algorithm. This does not require derivatives of the posterior density. Via a Monte Carlo method using simulated annealing | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Regarding the Expectation-Maximization algorithm, which one of the following false? | In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For an item that has not received any ratings, which method can make a prediction? | How does an analyst compare something rated a 1 to something rated a 2? Is one twice as good as the other? Again there is no theoretical way of aggregating the data. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For an item that has not received any ratings, which method can make a prediction? | How does an analyst compare something rated a 1 to something rated a 2? Is one twice as good as the other? Again there is no theoretical way of aggregating the data. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the following sentences: ```Aphrodite and Eros are Gods.``` ```Aphrodite is a parent of Eros.``` ```Aphrodite is beautiful.``` ```Aphrodite is happy.``` Specify which are the *classes*, the *instances* and the *properties* in the above statements. | However, in first-order logic, these two sentences may be couched as statements that a certain individual or non-logical object has a property. In this example, both sentences happen to have the common form isPhil ( x ) {\displaystyle {\text{isPhil}}(x)} for some individual x {\displaystyle x} , in the first sentence t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the following sentences: ```Aphrodite and Eros are Gods.``` ```Aphrodite is a parent of Eros.``` ```Aphrodite is beautiful.``` ```Aphrodite is happy.``` Specify which are the *classes*, the *instances* and the *properties* in the above statements. | These properties are formalized, statements (such as conditionals) are formed using them, and those statements taken together are the definition of the term. Consider a sentence such as "There's an electron in the sink." This means something along the lines of: "There exist some properties P1, P2, ..., Pn ( one for eve... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement Discounted Cumulative Gain. DCG is a retrieval metric that also takes into account the ordering of the result. The DCG accumulated at a rank $k$ is defined as: $DCG_k = \sum_{i=1}^k \frac{grade[i]}{log_2(i+1)}$ where $grade[i]$ is the relevance score given by the user for the result at position $i$. Hin... | DCG uses a graded relevance scale of documents from the result set to evaluate the usefulness, or gain, of a document based on its position in the result list. The premise of DCG is that highly relevant documents appearing lower in a search result list should be penalized as the graded relevance value is reduced logari... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement Discounted Cumulative Gain. DCG is a retrieval metric that also takes into account the ordering of the result. The DCG accumulated at a rank $k$ is defined as: $DCG_k = \sum_{i=1}^k \frac{grade[i]}{log_2(i+1)}$ where $grade[i]$ is the relevance score given by the user for the result at position $i$. Hin... | DCG uses a graded relevance scale of documents from the result set to evaluate the usefulness, or gain, of a document based on its position in the result list. The premise of DCG is that highly relevant documents appearing lower in a search result list should be penalized as the graded relevance value is reduced logari... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The SMART algorithm for query relevance feedback modifies? (Slide 11 Week 3) | To improve the quality of expansion words in pseudo-relevance feedback, a positional relevance feedback for pseudo-relevance feedback has been proposed to select from feedback documents those words that are focused on the query topic based on positions of words in feedback documents. Specifically, the positional releva... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The SMART algorithm for query relevance feedback modifies? (Slide 11 Week 3) | Clustering and Diversifying Web Search Results with Graph-Based Word Sense Induction. Computational Linguistics, 39(3), MIT Press, 2013, pp. 709–754. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Suppose that in a given FP Tree, an item in a leaf node N exists in every path. Which of the following is TRUE? | If every node of a tree has finitely many successors, then it is called a finitely, otherwise an infinitely branching tree. A path π is a subset of T such that ε ∈ π and for every t ∈ T, either t is a leaf or there exists a unique c ∈ N {\displaystyle \mathbb {N} } such that t.c ∈ π. A path may be a finite or infinite ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Suppose that in a given FP Tree, an item in a leaf node N exists in every path. Which of the following is TRUE? | The root is (s,0) and parent of a node (q,j) is (predecessor(q,j), j-1). This tree is infinite, finitely branching, and fully connected. Therefore, by Kőnig's lemma, there exists an infinite path (q0,0),(q1,1),(q2,2),... in the tree. Therefore, following is an accepting run of A run(q0,0)⋅run(q1,1)⋅run(q2,2)⋅...Hence, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In Ranked Retrieval, the result at position k is non-relevant and at k+1 is relevant. Which of the following is always true?Hint: P@k and R@k are the precision and recall of the result set consisting of the k top ranked documents. | For modern (web-scale) information retrieval, recall is no longer a meaningful metric, as many queries have thousands of relevant documents, and few users will be interested in reading all of them. Precision at k documents (P@k) is still a useful metric (e.g., P@10 or "Precision at 10" corresponds to the number of rele... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In Ranked Retrieval, the result at position k is non-relevant and at k+1 is relevant. Which of the following is always true?Hint: P@k and R@k are the precision and recall of the result set consisting of the k top ranked documents. | For modern (web-scale) information retrieval, recall is no longer a meaningful metric, as many queries have thousands of relevant documents, and few users will be interested in reading all of them. Precision at k documents (P@k) is still a useful metric (e.g., P@10 or "Precision at 10" corresponds to the number of rele... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Suppose that for points p, q, and t in metric space, the following hold:p is density-reachable from q t is density-reachable from qp is density-reachable from tWhich of the following statements is false? | The density theorem is usually proved using a simpler method (e.g. see Measure and Category). This theorem is also true for every finite Borel measure on Rn instead of Lebesgue measure (a proof can be found in e.g. (Ledrappier & Young 1985)). More generally, it is true of any finite Borel measure on a separable metric ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Suppose that for points p, q, and t in metric space, the following hold:p is density-reachable from q t is density-reachable from qp is density-reachable from tWhich of the following statements is false? | Reif and Tate prove that if the n-body reachability problem is defined as follows – given n bodies satisfying a fixed electrostatic potential law, determining if a body reaches a destination ball in a given time bound where we require a poly(n) bits of accuracy and the target time is poly(n) is in PSPACE. On the other ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If for the χ2 statistics for a binary feature, we obtain P(χ2 |DF = 1) < 0.05, this means: | χ 2 {\textstyle \chi ^{2}} values vs p {\displaystyle {\boldsymbol {p}}} -values The p-value is the probability of observing a test statistic at least as extreme in a chi-squared distribution. Accordingly, since the cumulative distribution function (CDF) for the appropriate degrees of freedom (df) gives the probability... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If for the χ2 statistics for a binary feature, we obtain P(χ2 |DF = 1) < 0.05, this means: | Because of this, one should expect the statistic to assume low values if x ¯ ≈ μ {\displaystyle {\overline {\mathbf {x} }}\approx {\boldsymbol {\mu }}} , and high values if they are different. From the distribution, t 2 ∼ T p , n − 1 2 = p ( n − 1 ) n − p F p , n − p , {\displaystyle t^{2}\sim T_{p,n-1}^{2}={\frac {p(n... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement a function that computes the support for each provided itemset by counting the number of its occurences in the original dataset of transactions. You can use the following formula: $$\mathrm{supp}(X) = \frac{|\{t \in T; X \subseteq t\}|}{|T|}$$ | Support is an indication of how frequently the itemset appears in the dataset. In our example, it can be easier to explain support by writing s u p p o r t = P ( A ∪ B ) = ( number of transactions containing A and B ) (total number of transactions) {\displaystyle support=P(A\cup B)={\frac {({\text{number of transaction... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement a function that computes the support for each provided itemset by counting the number of its occurences in the original dataset of transactions. You can use the following formula: $$\mathrm{supp}(X) = \frac{|\{t \in T; X \subseteq t\}|}{|T|}$$ | Assume that a large supermarket tracks sales data by stock-keeping unit (SKU) for each item: each item, such as "butter" or "bread", is identified by a numerical SKU. The supermarket has a database of transactions where each transaction is a set of SKUs that were bought together. Let the database of transactions consis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is false regarding K-means and DBSCAN? | DBSCAN clustering algorithm with Euclidean distance. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is false regarding K-means and DBSCAN? | Similar to k-means clustering, these "density attractors" can serve as representatives for the data set, but mean-shift can detect arbitrary-shaped clusters similar to DBSCAN. Due to the expensive iterative procedure and density estimation, mean-shift is usually slower than DBSCAN or k-Means. Besides that, the applicab... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is correct regarding community detection? | Much of the literature on algorithmic community detection addresses three statistical tasks: detection, partial recovery, and exact recovery. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is correct regarding community detection? | As pointed by the first work on community search published in SIGKDD'2010, many existing community detection/discovery methods consider the static community detection problem, where the graph needs to be partitioned a-priori with no reference to query nodes. While community search often focuses the most-likely communit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
We learnt in the lecture that terms are typically stored in an inverted list. Now, in the inverted list, instead of only storing document identifiers of the documents in which the term appears, assume we also store an *offset* of the appearance of a term in a document. An $offset$ of a term $l_k$ given a document is de... | A major drawback is that storing a word in the tree may require space beyond that required to store the word itself. An alternate representation is a suffix array, which is considered to require less virtual memory and supports data compression such as the BWT algorithm.Inverted index Stores a list of occurrences of ea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
We learnt in the lecture that terms are typically stored in an inverted list. Now, in the inverted list, instead of only storing document identifiers of the documents in which the term appears, assume we also store an *offset* of the appearance of a term in a document. An $offset$ of a term $l_k$ given a document is de... | A major drawback is that storing a word in the tree may require space beyond that required to store the word itself. An alternate representation is a suffix array, which is considered to require less virtual memory and supports data compression such as the BWT algorithm.Inverted index Stores a list of occurrences of ea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
When constructing a word embedding, negative samples are: | In natural language processing (NLP), a word embedding is a representation of a word. The embedding is used in text analysis. Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that words that are closer in the vector space are expected to be similar in meaning. Wor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
When constructing a word embedding, negative samples are: | Word embeddings may contain the biases and stereotypes contained in the trained dataset, as Bolukbasi et al. points out in the 2016 paper “Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings” that a publicly available (and popular) word2vec embedding trained on Google News texts (a commonl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following statements about index merging (when constructing inverted files) is correct? | The inverted index is filled via a merge or rebuild. A rebuild is similar to a merge but first deletes the contents of the inverted index. The architecture may be designed to support incremental indexing, where a merge identifies the document or documents to be added or updated and then parses each document into words.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following statements about index merging (when constructing inverted files) is correct? | The inverted index is filled via a merge or rebuild. A rebuild is similar to a merge but first deletes the contents of the inverted index. The architecture may be designed to support incremental indexing, where a merge identifies the document or documents to be added or updated and then parses each document into words.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For his awesome research, Tugrulcan is going to use the PageRank with teleportation and HITS algorithm, not on a network of webpages but on the retweet network of Twitter! The retweet network is a directed graph, where nodes are users and an edge going out from a user A and to a user B means that "User A retweeted User... | A Twitter bot is a computer program that can automatically tweet, retweet, and follow other accounts. Twitter's open application programming interface and the availability of cloud servers make it possible for Twitter bots to exist within the social networking site. Benign Twitter bots may generate creative content and... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For his awesome research, Tugrulcan is going to use the PageRank with teleportation and HITS algorithm, not on a network of webpages but on the retweet network of Twitter! The retweet network is a directed graph, where nodes are users and an edge going out from a user A and to a user B means that "User A retweeted User... | It is sometimes desirable to identify when a Twitter account is controlled by a internet bot. Following a test period, Twitter rolled out labels to identify bot accounts and automated tweets in February 2022.Detecting non-human Twitter users has been of interest to academics.In a 2012 paper, Chu et al. propose the foll... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $f_{\mathrm{MLP}}: \mathbb{R}^{d} \rightarrow \mathbb{R}$ be an $L$-hidden layer multi-layer perceptron (MLP) such that $$ f_{\mathrm{MLP}}(\mathbf{x})=\mathbf{w}^{\top} \sigma\left(\mathbf{W}_{L} \sigma\left(\mathbf{W}_{L-1} \ldots \sigma\left(\mathbf{W}_{1} \mathbf{x}\right)\right)\right) $$ with $\mathbf{w} \in ... | Consider a multilayer perceptron (MLP) with one hidden layer and m {\displaystyle m} hidden units with mapping from input x ∈ R d {\displaystyle x\in R^{d}} to a scalar output described as F x ( W ~ , Θ ) = ∑ i = 1 m θ i ϕ ( x T w ~ ( i ) ) {\displaystyle F_{x}({\tilde {W}},\Theta )=\sum _{i=1}^{m}\theta _{i}\phi (x^{T... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $f_{\mathrm{MLP}}: \mathbb{R}^{d} \rightarrow \mathbb{R}$ be an $L$-hidden layer multi-layer perceptron (MLP) such that $$ f_{\mathrm{MLP}}(\mathbf{x})=\mathbf{w}^{\top} \sigma\left(\mathbf{W}_{L} \sigma\left(\mathbf{W}_{L-1} \ldots \sigma\left(\mathbf{W}_{1} \mathbf{x}\right)\right)\right) $$ with $\mathbf{w} \in ... | Consider a multilayer perceptron (MLP) with one hidden layer and m {\displaystyle m} hidden units with mapping from input x ∈ R d {\displaystyle x\in R^{d}} to a scalar output described as F x ( W ~ , Θ ) = ∑ i = 1 m θ i ϕ ( x T w ~ ( i ) ) {\displaystyle F_{x}({\tilde {W}},\Theta )=\sum _{i=1}^{m}\theta _{i}\phi (x^{T... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a linear regression problem with $N$ samples $\left\{\left(\boldsymbol{x}_{n}, y_{n}\right)\right\}_{n=1}^{N}$, where each input $\boldsymbol{x}_{n}$ is a $D$-dimensional vector $\{-1,+1\}^{D}$, and all output values are $y_{i} \in \mathbb{R}$. Which of the following statements is correct? | In some models (standard linear regression, in particular), the equations for each of the data points i = 1, ..., n are stacked together and written in vector form as y = X β + ε , {\displaystyle \mathbf {y} =\mathbf {X} {\boldsymbol {\beta }}+{\boldsymbol {\varepsilon }},\,} where y = ( y 1 y 2 ⋮ y n ) , X = ( x 1 ′ x... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a linear regression problem with $N$ samples $\left\{\left(\boldsymbol{x}_{n}, y_{n}\right)\right\}_{n=1}^{N}$, where each input $\boldsymbol{x}_{n}$ is a $D$-dimensional vector $\{-1,+1\}^{D}$, and all output values are $y_{i} \in \mathbb{R}$. Which of the following statements is correct? | In some models (standard linear regression, in particular), the equations for each of the data points i = 1, ..., n are stacked together and written in vector form as y = X β + ε , {\displaystyle \mathbf {y} =\mathbf {X} {\boldsymbol {\beta }}+{\boldsymbol {\varepsilon }},\,} where y = ( y 1 y 2 ⋮ y n ) , X = ( x 1 ′ x... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
We apply a Gaussian Mixture Model made of $K$ isotropic Gaussians (invariant to rotation around its center) to $N$ vectors of dimension $D$. What is the number of \emph{free} parameters of this model?
| Gaussian mixture distributions are identifiable and commonly used for generative models. The parameterized joint distribution can be written as p ( x , y | θ ) = p ( y | θ ) p ( x | y , θ ) {\displaystyle p(x,y|\theta )=p(y|\theta )p(x|y,\theta )} by using the chain rule. Each parameter vector θ {\displaystyle \theta }... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
We apply a Gaussian Mixture Model made of $K$ isotropic Gaussians (invariant to rotation around its center) to $N$ vectors of dimension $D$. What is the number of \emph{free} parameters of this model?
| Gaussian mixture distributions are identifiable and commonly used for generative models. The parameterized joint distribution can be written as p ( x , y | θ ) = p ( y | θ ) p ( x | y , θ ) {\displaystyle p(x,y|\theta )=p(y|\theta )p(x|y,\theta )} by using the chain rule. Each parameter vector θ {\displaystyle \theta }... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recall that the hard-margin SVM problem corresponds to:
$$ \underset{\substack{\ww \in \R^d, \ orall i:\ y_i \ww^ op \xx_i \geq 1}}{\min} \Vert \ww \Vert_2.$$
Now consider the $2$-dimensional classification dataset corresponding to the $3$ following datapoints: $\xx_1 = (-1, 2)$, $\xx_2 = (1, 2)$, $\xx_3 = (0, -2)$ ... | Computing the (soft-margin) SVM classifier amounts to minimizing an expression of the form We focus on the soft-margin classifier since, as noted above, choosing a sufficiently small value for λ {\displaystyle \lambda } yields the hard-margin classifier for linearly classifiable input data. The classical approach, whic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recall that the hard-margin SVM problem corresponds to:
$$ \underset{\substack{\ww \in \R^d, \ orall i:\ y_i \ww^ op \xx_i \geq 1}}{\min} \Vert \ww \Vert_2.$$
Now consider the $2$-dimensional classification dataset corresponding to the $3$ following datapoints: $\xx_1 = (-1, 2)$, $\xx_2 = (1, 2)$, $\xx_3 = (0, -2)$ ... | Consider a binary classification problem with a dataset (x1, y1), ..., (xn, yn), where xi is an input vector and yi ∈ {-1, +1} is a binary label corresponding to it. A soft-margin support vector machine is trained by solving a quadratic programming problem, which is expressed in the dual form as follows: max α ∑ i = 1 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In this exercise, we will see how to combine the Principal Component Analysis (PCA) and the kernel method into an algorithm known as kernel PCA. We are given $n$ observations in a low dimensional space $\mathbf{x}_{1}, \cdots, \mathbf{x}_{n} \in \mathbb{R}^{L}$ and we consider a kernel $k$ and its associated features $... | Principal component analysis can be employed in a nonlinear way by means of the kernel trick. The resulting technique is capable of constructing nonlinear mappings that maximize the variance in the data. The resulting technique is called kernel PCA. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In this exercise, we will see how to combine the Principal Component Analysis (PCA) and the kernel method into an algorithm known as kernel PCA. We are given $n$ observations in a low dimensional space $\mathbf{x}_{1}, \cdots, \mathbf{x}_{n} \in \mathbb{R}^{L}$ and we consider a kernel $k$ and its associated features $... | In the field of multivariate statistics, kernel principal component analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $\mathcal{R}_{p}(f, \varepsilon)$ be the $\ell_{p}$ adversarial risk of a classifier $f: \mathbb{R}^{d} \rightarrow\{ \pm 1\}$, i.e., $$ \mathcal{R}_{p}(f, \varepsilon)=\mathbb{E}_{(\mathbf{x}, y) \sim \mathcal{D}}\left[\max _{\tilde{\mathbf{x}}:\|\mathbf{x}-\tilde{\mathbf{x}}\|_{p} \leq \varepsilon} \mathbb{1}_{\{... | Assume the VC-dimension of the underlying base classifier is d {\displaystyle d} and m ≥ d ≥ 1 {\displaystyle m\geq d\geq 1} . Then with probability 1 − δ {\displaystyle 1-\delta } we have the bound P D ( y ∑ j t α j h j ( x ) ∑ | α j | ≤ 0 ) ≤ P S ( y ∑ j t α j h j ( x ) ∑ | α j | ≤ θ ) + O ( 1 m d log 2 ( m / d ) /... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $\mathcal{R}_{p}(f, \varepsilon)$ be the $\ell_{p}$ adversarial risk of a classifier $f: \mathbb{R}^{d} \rightarrow\{ \pm 1\}$, i.e., $$ \mathcal{R}_{p}(f, \varepsilon)=\mathbb{E}_{(\mathbf{x}, y) \sim \mathcal{D}}\left[\max _{\tilde{\mathbf{x}}:\|\mathbf{x}-\tilde{\mathbf{x}}\|_{p} \leq \varepsilon} \mathbb{1}_{\{... | Fix a loss function L: Y × Y → R ≥ 0 {\displaystyle {\mathcal {L}}\colon Y\times Y\to \mathbb {R} _{\geq 0}} , for example, the square loss L ( y , y ′ ) = ( y − y ′ ) 2 {\displaystyle {\mathcal {L}}(y,y')=(y-y')^{2}} , where h ( x ) = y ′ {\displaystyle h(x)=y'} . For a given distribution ρ {\displaystyle \rho } on X ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The following function(s) have a unique minimizer. | So the algorithm can be slightly revised as follows. minimize V ( w → , ξ → ) = 1 2 w → ⋅ w → + constant ⋅ ∑ ξ i , j , k subject to ∀ ξ i , j , k ≧ 0 ∀ ( c i , c j ) ∈ r k ′ w → ( Φ ( q 1 , c i ) − Φ ( q 1 , c j ) ) ≧ 1 − ξ i , j , 1 ; ⋮ w → ( Φ ( q n , c i ) − Φ ( q n , c j ) ) ≧ 1 − ξ i , j , n ; where k ∈ { 1 , 2 , ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The following function(s) have a unique minimizer. | The goal is to minimize ∑ i = 1 m ∑ j = 1 n t i , j x i , j {\displaystyle \sum \limits _{i=1}^{m}\sum \limits _{j=1}^{n}t_{i,j}x_{i,j}} subject to: x r , s ≥ 0 {\displaystyle x_{r,s}\geq 0} ; ∀ r = 1 … m {\displaystyle \forall r=1\ldots m} , s = 1 … n {\displaystyle s=1\ldots n} ∑ s = 1 m + n x i , s − ∑ r = 1 m + n x... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
We will analyze the $K$-means algorithm and show that it always converge. Let us consider the $K$-means objective function: $$ \mathcal{L}(\mathbf{z}, \boldsymbol{\mu})=\sum_{n=1}^{N} \sum_{k=1}^{K} z_{n k}\left\|\mathbf{x}_{n}-\boldsymbol{\mu}_{k}\right\|_{2}^{2} $$ where $z_{n k} \in\{0,1\}$ with $\sum_{k=1}^{K} z_{n... | It can be shown that the algorithm will terminate in a finite number of iterations (no more than the total number of possible assignments, which is bounded by k m {\displaystyle k^{m}} ). In addition, the algorithm will terminate at a point that the overall objective cannot be decreased either by a different assignment... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
We will analyze the $K$-means algorithm and show that it always converge. Let us consider the $K$-means objective function: $$ \mathcal{L}(\mathbf{z}, \boldsymbol{\mu})=\sum_{n=1}^{N} \sum_{k=1}^{K} z_{n k}\left\|\mathbf{x}_{n}-\boldsymbol{\mu}_{k}\right\|_{2}^{2} $$ where $z_{n k} \in\{0,1\}$ with $\sum_{k=1}^{K} z_{n... | Given a set of observations (x1, x2, ..., xn), where each observation is a d-dimensional real vector, k-means clustering aims to partition the n observations into k (≤ n) sets S = {S1, S2, ..., Sk} so as to minimize the within-cluster sum of squares (WCSS) (i.e. variance). Formally, the objective is to find: where μi i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
(Stochastic Gradient Descent) One iteration of standard SGD for SVM, logistic regression and ridge regression costs roughly $\mathcal{O}(D)$, where $D$ is the dimension of a data point. | Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of gradient descent optimization, since it replaces the actual gradient (calcul... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
(Stochastic Gradient Descent) One iteration of standard SGD for SVM, logistic regression and ridge regression costs roughly $\mathcal{O}(D)$, where $D$ is the dimension of a data point. | A conceptually simple extension of stochastic gradient descent makes the learning rate a decreasing function ηt of the iteration number t, giving a learning rate schedule, so that the first iterations cause large changes in the parameters, while the later ones do only fine-tuning. Such schedules have been known since t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the following joint distribution that has the factorization $$ p\left(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\right)=p\left(x_{1}\right) p\left(x_{2} \mid x_{1}\right) p\left(x_{3} \mid x_{2}\right) p\left(x_{4} \mid x_{1}, x_{3}\right) p\left(x_{5} \mid x_{4}\right) . $$ We say that a data point $y$ follows a Poiss... | We model a set of observations as a random sample from an unknown joint probability distribution which is expressed in terms of a set of parameters. The goal of maximum likelihood estimation is to determine the parameters for which the observed data have the highest joint probability. We write the parameters governing ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the following joint distribution that has the factorization $$ p\left(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\right)=p\left(x_{1}\right) p\left(x_{2} \mid x_{1}\right) p\left(x_{3} \mid x_{2}\right) p\left(x_{4} \mid x_{1}, x_{3}\right) p\left(x_{5} \mid x_{4}\right) . $$ We say that a data point $y$ follows a Poiss... | {\displaystyle p({\bf {y}},\theta |{\bf {x}})\;=\;p({\bf {y}}|{\bf {x}},\theta )p(\theta )\;=\;p({\bf {y}}|{\bf {x}})p(\theta |{\bf {y}},{\bf {x}})\;\simeq \;{\tilde {q}}(\theta )\;=\;Zq(\theta ).} The joint is equal to the product of the likelihood and the prior and by Bayes' rule, equal to the product of the marginal... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider two fully connected networks, A and B, with a constant width for all layers, inputs and outputs. Network A has depth $3L$ and width $H$, network B has depth $L$ and width $2H$. Everything else is identical for the two networks and both $L$ and $H$ are large. In this case, performing a single iteration of backp... | The universal approximation property of width-bounded networks has been studied as a dual of classical universal approximation results on depth-bounded networks. For input dimension dx and output dimension dy the minimum width required for the universal approximation of the Lp functions is exactly max{dx + 1, dy} (for ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider two fully connected networks, A and B, with a constant width for all layers, inputs and outputs. Network A has depth $3L$ and width $H$, network B has depth $L$ and width $2H$. Everything else is identical for the two networks and both $L$ and $H$ are large. In this case, performing a single iteration of backp... | In the same paper it was shown that ReLU networks with width n + 1 were sufficient to approximate any continuous function of n-dimensional input variables. The following refinement, specifies the optimal minimum width for which such an approximation is possible and is due to. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Now let $\xv$ be a random vector distributed according to the uniform distribution over the finite centered dataset $\xv_1, . . . , \xv_N$ from above. %
Consider the problem of finding a unit vector, $\wv \in \R^D$, such that the random variable $\wv^ op \xx$ has \emph{maximal} variance. What does it mean for the data ... | A real random vector X = ( X 1 , … , X k ) T {\displaystyle \mathbf {X} =(X_{1},\ldots ,X_{k})^{\mathrm {T} }} is called a centered normal random vector if there exists a deterministic k × ℓ {\displaystyle k\times \ell } matrix A {\displaystyle {\boldsymbol {A}}} such that A Z {\displaystyle {\boldsymbol {A}}\mathbf {Z... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Now let $\xv$ be a random vector distributed according to the uniform distribution over the finite centered dataset $\xv_1, . . . , \xv_N$ from above. %
Consider the problem of finding a unit vector, $\wv \in \R^D$, such that the random variable $\wv^ op \xx$ has \emph{maximal} variance. What does it mean for the data ... | Given a column-vector, v {\displaystyle \mathbf {v} \,} of size n, the centering property of C n {\displaystyle C_{n}\,} can be expressed as C n v = v − ( 1 n J n , 1 T v ) J n , 1 {\displaystyle C_{n}\,\mathbf {v} =\mathbf {v} -({\tfrac {1}{n}}J_{n,1}^{\textrm {T}}\mathbf {v} )J_{n,1}} where J n , 1 {\displaystyle J_{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a regression task. You are using your favorite learning algorithm with parameters w and add a regularization term of the form $\frac{\lambda}{2}\|\mathbf{w}\|^{2}$. Which of the following statements are correct for a typical scenario? | Choosing the regularization parameter ( λ {\displaystyle \lambda } ) is a fundamental part of lasso. A good value is essential to the performance of lasso since it controls the strength of shrinkage and variable selection, which, in moderation can improve both prediction accuracy and interpretability. However, if the r... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a regression task. You are using your favorite learning algorithm with parameters w and add a regularization term of the form $\frac{\lambda}{2}\|\mathbf{w}\|^{2}$. Which of the following statements are correct for a typical scenario? | A regularization term (or regularizer) R ( f ) {\displaystyle R(f)} is added to a loss function: min f ∑ i = 1 n V ( f ( x i ) , y i ) + λ R ( f ) {\displaystyle \min _{f}\sum _{i=1}^{n}V(f(x_{i}),y_{i})+\lambda R(f)} where V {\displaystyle V} is an underlying loss function that describes the cost of predicting f ( x )... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a movie recommendation system which minimizes the following objective
rac{1}{2} \sum_{(d,n)\in\Omega} [x_{dn} - (\mathbf{W} \mathbf{Z}^ op)_{dn}]^2 + rac{\lambda_w}{2}
orm{\mathbf{W}}_ ext{Frob}^2 + rac{\lambda_z}{2}
orm{\mathbf{Z}}_ ext{Frob}^2
where $\mathbf{W}\in \R^{D imes K}$ and $\ma... | Many standard NMF algorithms analyze all the data together; i.e., the whole matrix is available from the start. This may be unsatisfactory in applications where there are too many data to fit into memory or where the data are provided in streaming fashion. One such use is for collaborative filtering in recommendation s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a movie recommendation system which minimizes the following objective
rac{1}{2} \sum_{(d,n)\in\Omega} [x_{dn} - (\mathbf{W} \mathbf{Z}^ op)_{dn}]^2 + rac{\lambda_w}{2}
orm{\mathbf{W}}_ ext{Frob}^2 + rac{\lambda_z}{2}
orm{\mathbf{Z}}_ ext{Frob}^2
where $\mathbf{W}\in \R^{D imes K}$ and $\ma... | R ( f 1 ⋯ f T ) = ∑ r = 1 C ∑ t ∈ I ( r ) ‖ f t − 1 I ( r ) ∑ s ∈ I ( r ) f s ‖ H k 2 {\displaystyle R(f_{1}\cdots f_{T})=\sum _{r=1}^{C}\sum _{t\in I(r)}\|f_{t}-{\frac {1}{I(r)}}\sum _{s\in I(r)}f_{s}\|_{H_{k}}^{2}} where I ( r ) {\displaystyle I(r)} is a cluster of tasks.This regularizer is similar to the mean-constr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
(SVD) The set of singular values of any rectangular matrix $\mathbf{X}$ is equal to the set of eigenvalues for the square matrix $\mathbf{X X}^{\top}$. | Perform the singular value decomposition (SVD) of the trajectory matrix X {\displaystyle \mathbf {X} } . Set S = X X T {\displaystyle \mathbf {S} =\mathbf {X} \mathbf {X} ^{\mathrm {T} }} and denote by λ 1 , … , λ L {\displaystyle \lambda _{1},\ldots ,\lambda _{L}} the eigenvalues of S {\displaystyle \mathbf {S} } take... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
(SVD) The set of singular values of any rectangular matrix $\mathbf{X}$ is equal to the set of eigenvalues for the square matrix $\mathbf{X X}^{\top}$. | Applying singular-value decomposition (SVD) to matrix A {\displaystyle A} with dimensions p × m {\displaystyle p\times m} produces a singular system consisting of singular values { σ j } j = 1 k , ( σ j > 0 ∀ j = 1 , … , k ) , {\displaystyle \{\sigma _{j}\}_{j=1}^{k},{\text{ }}(\sigma _{j}>0{\text{ }}\forall j=1,\dots ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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