pwc-archive/papers-with-abstracts huggingface dataset:
A Fourier Approach to the Parameter Estimation Problem for One-dimensional Gaussian Mixture Models
Authors: Xinyu Liu, Hai Zhang
Date: 2024-04-19 00:00:00
Tasks: parameter estimation

The purpose of this paper is twofold. First, we propose a novel algorithm for estimating parameters in one-dimensional Gaussian mixture models (GMMs). The algorithm takes advantage of the Hankel structure inherent in the Fourier data obtained from independent and identically distributed (i.i.d) samples of the mixture. For GMMs with a unified variance, a singular value ratio functional using the Fourier data is introduced and used to resolve the variance and component number simultaneously. The consistency of the estimator is derived. Compared to classic algorithms such as the method of moments and the maximum likelihood method, the proposed algorithm does not require prior knowledge of the number of Gaussian components or good initial guesses. Numerical experiments demonstrate its superior performance in estimation accuracy and computational cost. Second, we reveal that there exists a fundamental limit to the problem of estimating the number of Gaussian components or model order in the mixture model if the number of i.i.d samples is finite. For the case of a single variance, we show that the model order can be successfully estimated only if the minimum separation distance between the component means exceeds a certain threshold value and can fail if below. We derive a lower bound for this threshold value, referred to as the computational resolution limit, in terms of the number of i.i.d samples, the variance, and the number of Gaussian components. Numerical experiments confirm this phase transition phenomenon in estimating the model order. Moreover, we demonstrate that our algorithm achieves better scores in likelihood, AIC, and BIC when compared to the EM algorithm.
Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penalty
Authors: Yanwei Jia
Date: 2024-04-19 00:00:00
Tasks: Q-Learning, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL)

This paper studies continuous-time risk-sensitive reinforcement learning (RL) under the entropy-regularized, exploratory diffusion process formulation with the exponential-form objective. The risk-sensitive objective arises either as the agent's risk attitude or as a distributionally robust approach against the model uncertainty. Owing to the martingale perspective in Jia and Zhou (2023) the risk-sensitive RL problem is shown to be equivalent to ensuring the martingale property of a process involving both the value function and the q-function, augmented by an additional penalty term: the quadratic variation of the value process, capturing the variability of the value-to-go along the trajectory. This characterization allows for the straightforward adaptation of existing RL algorithms developed for non-risk-sensitive scenarios to incorporate risk sensitivity by adding the realized variance of the value process. Additionally, I highlight that the conventional policy gradient representation is inadequate for risk-sensitive problems due to the nonlinear nature of quadratic variation; however, q-learning offers a solution and extends to infinite horizon settings. Finally, I prove the convergence of the proposed algorithm for Merton's investment problem and quantify the impact of temperature parameter on the behavior of the learning procedure. I also conduct simulation experiments to demonstrate how risk-sensitive RL improves the finite-sample performance in the linear-quadratic control problem.
The phase diagram of kernel interpolation in large dimensions
Authors: Haobo Zhang, Weihao Lu, Qian Lin
Date: 2024-04-19 00:00:00

The generalization ability of kernel interpolation in large dimensions (i.e., $n \asymp d^{\gamma}$ for some $\gamma>0$) might be one of the most interesting problems in the recent renaissance of kernel regression, since it may help us understand the 'benign overfitting phenomenon' reported in the neural networks literature. Focusing on the inner product kernel on the sphere, we fully characterized the exact order of both the variance and bias of large-dimensional kernel interpolation under various source conditions $s\geq 0$. Consequently, we obtained the $(s,\gamma)$-phase diagram of large-dimensional kernel interpolation, i.e., we determined the regions in $(s,\gamma)$-plane where the kernel interpolation is minimax optimal, sub-optimal and inconsistent.
Risk Bounds for Mixture Density Estimation on Compact Domains via the $h$-Lifted Kullback--Leibler Divergence
Authors: Mark Chiu Chong, Hien Duy Nguyen, TrungTin Nguyen
Date: 2024-04-19 00:00:00
Tasks: Density Estimation

We consider the problem of estimating probability density functions based on sample data, using a finite mixture of densities from some component class. To this end, we introduce the $h$-lifted Kullback--Leibler (KL) divergence as a generalization of the standard KL divergence and a criterion for conducting risk minimization. Under a compact support assumption, we prove an $\mathcal{O}(1/{\sqrt{n}})$ bound on the expected estimation error when using the $h$-lifted KL divergence, which extends the results of Rakhlin et al. (2005, ESAIM: Probability and Statistics, Vol. 9) and Li and Barron (1999, Advances in Neural Information ProcessingSystems, Vol. 12) to permit the risk bounding of density functions that are not strictly positive. We develop a procedure for the computation of the corresponding maximum $h$-lifted likelihood estimators ($h$-MLLEs) using the Majorization-Maximization framework and provide experimental results in support of our theoretical bounds.
On the use of adversarial validation for quantifying dissimilarity in geospatial machine learning prediction
Authors: Yanwen Wang, Mahdi Khodadadzadeh, Raul Zurita-Milla
Date: 2024-04-19 00:00:00

Recent geospatial machine learning studies have shown that the results of model evaluation via cross-validation (CV) are strongly affected by the dissimilarity between the sample data and the prediction locations. In this paper, we propose a method to quantify such a dissimilarity in the interval 0 to 100%, and from the perspective of the data feature space. The proposed method is based on adversarial validation, which is an approach that can check whether sample data and prediction locations can be separated with a binary classifier. To study the effectiveness and generality of our method, we tested it on a series of experiments based on both synthetic and real datasets and with gradually increasing dissimilarities. Results show that the proposed method can successfully quantify dissimilarity across the entire range of values. Next to this, we studied how dissimilarity affects CV evaluations by comparing the results of random CV and of two spatial CV methods, namely block and spatial+ CV. Our results showed that CV evaluations follow similar patterns in all datasets and predictions: when dissimilarity is low (usually lower than 30%), random CV provides the most accurate evaluation results. As dissimilarity increases, spatial CV methods, especially spatial+ CV, become more and more accurate and even outperforming random CV. When dissimilarity is high (>=90%), no CV method provides accurate evaluations. These results show the importance of considering feature space dissimilarity when working with geospatial machine learning predictions, and can help researchers and practitioners to select more suitable CV methods for evaluating their predictions.
Learning Stable and Passive Neural Differential Equations
Authors: Jing Cheng, Ruigang Wang, Ian R. Manchester
Date: 2024-04-19 00:00:00

In this paper, we introduce a novel class of neural differential equation, which are intrinsically Lyapunov stable, exponentially stable or passive. We take a recently proposed Polyak Lojasiewicz network (PLNet) as an Lyapunov function and then parameterize the vector field as the descent directions of the Lyapunov function. The resulting models have a same structure as the general Hamiltonian dynamics, where the Hamiltonian is lower- and upper-bounded by quadratic functions. Moreover, it is also positive definite w.r.t. either a known or learnable equilibrium. We illustrate the effectiveness of the proposed model on a damped double pendulum system.
Beyond development: Challenges in deploying machine learning models for structural engineering applications
Authors: Mohsen Zaker Esteghamati, Brennan Bean, Henry V. Burton, M. Z. Naser
Date: 2024-04-18 00:00:00
Tasks: feature selection

Machine learning (ML)-based solutions are rapidly changing the landscape of many fields, including structural engineering. Despite their promising performance, these approaches are usually only demonstrated as proof-of-concept in structural engineering, and are rarely deployed for real-world applications. This paper aims to illustrate the challenges of developing ML models suitable for deployment through two illustrative examples. Among various pitfalls, the presented discussion focuses on model overfitting and underspecification, training data representativeness, variable omission bias, and cross-validation. The results highlight the importance of implementing rigorous model validation techniques through adaptive sampling, careful physics-informed feature selection, and considerations of both model complexity and generalizability.
TrajDeleter: Enabling Trajectory Forgetting in Offline Reinforcement Learning Agents
Authors: Chen Gong, Kecen Li, Jin Yao, Tianhao Wang
Date: 2024-04-18 00:00:00
Tasks: energy management, Offline RL, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL)

Reinforcement learning (RL) trains an agent from experiences interacting with the environment. In scenarios where online interactions are impractical, offline RL, which trains the agent using pre-collected datasets, has become popular. While this new paradigm presents remarkable effectiveness across various real-world domains, like healthcare and energy management, there is a growing demand to enable agents to rapidly and completely eliminate the influence of specific trajectories from both the training dataset and the trained agents. To meet this problem, this paper advocates Trajdeleter, the first practical approach to trajectory unlearning for offline RL agents. The key idea of Trajdeleter is to guide the agent to demonstrate deteriorating performance when it encounters states associated with unlearning trajectories. Simultaneously, it ensures the agent maintains its original performance level when facing other remaining trajectories. Additionally, we introduce Trajauditor, a simple yet efficient method to evaluate whether Trajdeleter successfully eliminates the specific trajectories of influence from the offline RL agent. Extensive experiments conducted on six offline RL algorithms and three tasks demonstrate that Trajdeleter requires only about 1.5% of the time needed for retraining from scratch. It effectively unlearns an average of 94.8% of the targeted trajectories yet still performs well in actual environment interactions after unlearning. The replication package and agent parameters are available online.
Generalizing Machine Learning Evaluation through the Integration of Shannon Entropy and Rough Set Theory
Authors: Olga Cherednichenko, Dmytro Chernyshov, Dmytro Sytnikov, Polina Sytnikova
Date: 2024-04-18 00:00:00
Tasks: Decision Making, Model Selection, Uncertainty Quantification

This research paper delves into the innovative integration of Shannon entropy and rough set theory, presenting a novel approach to generalize the evaluation approach in machine learning. The conventional application of entropy, primarily focused on information uncertainty, is extended through its combination with rough set theory to offer a deeper insight into data's intrinsic structure and the interpretability of machine learning models. We introduce a comprehensive framework that synergizes the granularity of rough set theory with the uncertainty quantification of Shannon entropy, applied across a spectrum of machine learning algorithms. Our methodology is rigorously tested on various datasets, showcasing its capability to not only assess predictive performance but also to illuminate the underlying data complexity and model robustness. The results underscore the utility of this integrated approach in enhancing the evaluation landscape of machine learning, offering a multi-faceted perspective that balances accuracy with a profound understanding of data attributes and model dynamics. This paper contributes a groundbreaking perspective to machine learning evaluation, proposing a method that encapsulates a holistic view of model performance, thereby facilitating more informed decision-making in model selection and application.
Neural Methods for Amortized Inference
Authors: Andrew Zammit-Mangion, Matthew Sainsbury-Dale, Raphaël Huser
Date: 2024-04-18 00:00:00
Tasks: Bayesian Inference

Simulation-based methods for statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The field is undergoing a new revolution as it embraces the representational capacity of neural networks, optimization libraries and graphics processing units for learning complex mappings between data and inferential targets. The resulting tools are amortized, in the sense that, after an initial setup cost, they allow rapid inference through fast feed-forward operations. In this article we review recent progress in the context of point estimation, approximate Bayesian inference, summary-statistic construction, and likelihood approximation. We also cover software, and include a simple illustration to showcase the wide array of tools available for amortized inference and the benefits they offer over Markov chain Monte Carlo methods. The article concludes with an overview of relevant topics and an outlook on future research directions.
Understanding Optimal Feature Transfer via a Fine-Grained Bias-Variance Analysis
Authors: Yufan Li, Subhabrata Sen, Ben Adlam
Date: 2024-04-18 00:00:00
Tasks: Transfer Learning

In the transfer learning paradigm models learn useful representations (or features) during a data-rich pretraining stage, and then use the pretrained representation to improve model performance on data-scarce downstream tasks. In this work, we explore transfer learning with the goal of optimizing downstream performance. We introduce a simple linear model that takes as input an arbitrary pretrained feature transform. We derive exact asymptotics of the downstream risk and its \textit{fine-grained} bias-variance decomposition. We then identify the pretrained representation that optimizes the asymptotic downstream bias and variance averaged over an ensemble of downstream tasks. Our theoretical and empirical analysis uncovers the surprising phenomenon that the optimal featurization is naturally sparse, even in the absence of explicit sparsity-inducing priors or penalties. Additionally, we identify a phase transition where the optimal pretrained representation shifts from hard selection to soft selection of relevant features.
A New Reliable & Parsimonious Learning Strategy Comprising Two Layers of Gaussian Processes, to Address Inhomogeneous Empirical Correlation Structures
Authors: Gargi Roy, Dalia Chakrabarty
Date: 2024-04-18 00:00:00
Tasks: Gaussian Processes

We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data, by modelling the sought function as a sample function of a non-stationary Gaussian Process (GP), that nests within itself multiple other GPs, each of which we prove can be stationary, thereby establishing sufficiency of two GP layers. In fact, a non-stationary kernel is envisaged, with each hyperparameter set as dependent on the sample function drawn from the outer non-stationary GP, such that a new sample function is drawn at every pair of input values at which the kernel is computed. However, such a model cannot be implemented, and we substitute this by recalling that the average effect of drawing different sample functions from a given GP is equivalent to that of drawing a sample function from each of a set of GPs that are rendered different, as updated during the equilibrium stage of the undertaken inference (via MCMC). The kernel is fully non-parametric, and it suffices to learn one hyperparameter per layer of GP, for each dimension of the input variable. We illustrate this new learning strategy on a real dataset.
RAGCache: Efficient Knowledge Caching for Retrieval-Augmented Generation
Authors: Chao Jin, Zili Zhang, Xuanlin Jiang, Fangyue Liu, Xin Liu, Xuanzhe Liu, Xin Jin
Date: 2024-04-18 00:00:00
Tasks: GPU, RAG, Retrieval, Retrieval-augmented Generation

Retrieval-Augmented Generation (RAG) has shown significant improvements in various natural language processing tasks by integrating the strengths of large language models (LLMs) and external knowledge databases. However, RAG introduces long sequence generation and leads to high computation and memory costs. We propose RAGCache, a novel multilevel dynamic caching system tailored for RAG. Our analysis benchmarks current RAG systems, pinpointing the performance bottleneck (i.e., long sequence due to knowledge injection) and optimization opportunities (i.e., caching knowledge's intermediate states). Based on these insights, we design RAGCache, which organizes the intermediate states of retrieved knowledge in a knowledge tree and caches them in the GPU and host memory hierarchy. RAGCache proposes a replacement policy that is aware of LLM inference characteristics and RAG retrieval patterns. It also dynamically overlaps the retrieval and inference steps to minimize the end-to-end latency. We implement RAGCache and evaluate it on vLLM, a state-of-the-art LLM inference system and Faiss, a state-of-the-art vector database. The experimental results show that RAGCache reduces the time to first token (TTFT) by up to 4x and improves the throughput by up to 2.1x compared to vLLM integrated with Faiss.
Adaptive Catalyst Discovery Using Multicriteria Bayesian Optimization with Representation Learning
Authors: Jie Chen, Pengfei Ou, Yuxin Chang, Hengrui Zhang, Xiao-Yan Li, Edward H. Sargent, Wei Chen
Date: 2024-04-18 00:00:00
Tasks: Bayesian Optimization, Representation Learning, Uncertainty Quantification

High-performance catalysts are crucial for sustainable energy conversion and human health. However, the discovery of catalysts faces challenges due to the absence of efficient approaches to navigating vast and high-dimensional structure and composition spaces. In this study, we propose a high-throughput computational catalyst screening approach integrating density functional theory (DFT) and Bayesian Optimization (BO). Within the BO framework, we propose an uncertainty-aware atomistic machine learning model, UPNet, which enables automated representation learning directly from high-dimensional catalyst structures and achieves principled uncertainty quantification. Utilizing a constrained expected improvement acquisition function, our BO framework simultaneously considers multiple evaluation criteria. Using the proposed methods, we explore catalyst discovery for the CO2 reduction reaction. The results demonstrate that our approach achieves high prediction accuracy, facilitates interpretable feature extraction, and enables multicriteria design optimization, leading to significant reduction of computing power and time (10x reduction of required DFT calculations) in high-performance catalyst discovery.
The graph alignment problem: fundamental limits and efficient algorithms
Authors: Luca Ganassali
Date: 2024-04-18 00:00:00

This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the graphs are random, we are interested in understanding the fundamental information-theoretical limits for this problem, as well as designing and analyzing algorithms that are able to recover the underlying alignment in the data. For these algorithms, we give some high probability guarantees on the regime in which they succeed or fail.
Full Shot Predictions for the DIII-D Tokamak via Deep Recurrent Networks
Authors: Ian Char, Youngseog Chung, Joseph Abbate, Egemen Kolemen, Jeff Schneider
Date: 2024-04-18 00:00:00

Although tokamaks are one of the most promising devices for realizing nuclear fusion as an energy source, there are still key obstacles when it comes to understanding the dynamics of the plasma and controlling it. As such, it is crucial that high quality models are developed to assist in overcoming these obstacles. In this work, we take an entirely data driven approach to learn such a model. In particular, we use historical data from the DIII-D tokamak to train a deep recurrent network that is able to predict the full time evolution of plasma discharges (or "shots"). Following this, we investigate how different training and inference procedures affect the quality and calibration of the shot predictions.
Sample Design Engineering: An Empirical Study of What Makes Good Downstream Fine-Tuning Samples for LLMs
Authors: Biyang Guo, He Wang, Wenyilin Xiao, Hong Chen, Zhuxin Lee, Songqiao Han, Hailiang Huang
Date: 2024-04-19 00:00:00
Tasks: Event Extraction, In-Context Learning, Prompt Engineering, Sentiment Analysis

In the burgeoning field of Large Language Models (LLMs) like ChatGPT and LLaMA, Prompt Engineering (PE) is renowned for boosting zero-shot or in-context learning (ICL) through prompt modifications. Yet, the realm of the sample design for downstream fine-tuning, crucial for task-specific LLM adaptation, is largely unexplored. This paper introduces Sample Design Engineering (SDE), a methodical approach to enhancing LLMs' post-tuning performance by refining input, output, and reasoning designs. We conduct a series of in-domain (ID) and out-of-domain (OOD) experiments to assess the impact of various design options on LLMs' downstream performance, revealing several intriguing patterns that hold consistently across different LLMs. Based on these insights, we propose an integrated SDE strategy, combining the most effective options, and validate its consistent superiority over heuristic sample designs in complex downstream tasks like multi-aspect sentiment analysis, event extraction, and nested entity recognition. Additionally, analyses of LLMs' inherent prompt/output perplexity, zero-shot, and ICL abilities illustrate that good PE strategies may not always translate to good SDE strategies. Code available at https://github.com/beyondguo/LLM-Tuning.