pwc-archive/papers-with-abstracts huggingface dataset:
A convex formulation of covariate-adjusted Gaussian graphical models via natural parametrization
Authors: Ruobin Liu, Guo Yu
Date: 2024-10-08 00:00:00

Gaussian graphical models (GGMs) are widely used for recovering the conditional independence structure among random variables. Recently, several key advances have been made to exploit an additional set of variables for better estimating the GGMs of the variables of interest. For example, in co-expression quantitative trait locus (eQTL) studies, both the mean expression level of genes as well as their pairwise conditional independence structure may be adjusted by genetic variants local to those genes. Existing methods to estimate covariate-adjusted GGMs either allow only the mean to depend on covariates or suffer from poor scaling assumptions due to the inherent non-convexity of simultaneously estimating the mean and precision matrix. In this paper, we propose a convex formulation that jointly estimates the covariate-adjusted mean and precision matrix by utilizing the natural parametrization of the multivariate Gaussian likelihood. This convexity yields theoretically better performance as the sparsity and dimension of the covariates grow large relative to the number of samples. We verify our theoretical results with numerical simulations and perform a reanalysis of an eQTL study of glioblastoma multiforme (GBM), an aggressive form of brain cancer.
On the Impacts of the Random Initialization in the Neural Tangent Kernel Theory
Authors: Guhan Chen, Yicheng Li, Qian Lin
Date: 2024-10-08 00:00:00

This paper aims to discuss the impact of random initialization of neural networks in the neural tangent kernel (NTK) theory, which is ignored by most recent works in the NTK theory. It is well known that as the network's width tends to infinity, the neural network with random initialization converges to a Gaussian process $f^{\mathrm{GP}}$, which takes values in $L^{2}(\mathcal{X})$, where $\mathcal{X}$ is the domain of the data. In contrast, to adopt the traditional theory of kernel regression, most recent works introduced a special mirrored architecture and a mirrored (random) initialization to ensure the network's output is identically zero at initialization. Therefore, it remains a question whether the conventional setting and mirrored initialization would make wide neural networks exhibit different generalization capabilities. In this paper, we first show that the training dynamics of the gradient flow of neural networks with random initialization converge uniformly to that of the corresponding NTK regression with random initialization $f^{\mathrm{GP}}$. We then show that $\mathbf{P}(f^{\mathrm{GP}} \in [\mathcal{H}^{\mathrm{NT}}]^{s}) = 1$ for any $s < \frac{3}{d+1}$ and $\mathbf{P}(f^{\mathrm{GP}} \in [\mathcal{H}^{\mathrm{NT}}]^{s}) = 0$ for any $s \geq \frac{3}{d+1}$, where $[\mathcal{H}^{\mathrm{NT}}]^{s}$ is the real interpolation space of the RKHS $\mathcal{H}^{\mathrm{NT}}$ associated with the NTK. Consequently, the generalization error of the wide neural network trained by gradient descent is $\Omega(n^{-\frac{3}{d+3}})$, and it still suffers from the curse of dimensionality. On one hand, the result highlights the benefits of mirror initialization. On the other hand, it implies that NTK theory may not fully explain the superior performance of neural networks.
The Breakdown of Gaussian Universality in Classification of High-dimensional Linear Factor Mixtures
Authors: Xiaoyi Mai, Zhenyu Liao
Date: 2024-10-08 00:00:00

The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To relax this restrictive assumption, subsequent efforts have been devoted to establish "Gaussian equivalent principles" by studying scenarios of Gaussian universality where the asymptotic performance of ML methods on non-Gaussian data remains unchanged when replaced with Gaussian data having the same mean and covariance. Beyond the realm of Gaussian universality, there are few exact results on how the data distribution affects the learning performance. In this article, we provide a precise high-dimensional characterization of empirical risk minimization, for classification under a general mixture data setting of linear factor models that extends Gaussian mixtures. The Gaussian universality is shown to break down under this setting, in the sense that the asymptotic learning performance depends on the data distribution beyond the class means and covariances. To clarify the limitations of Gaussian universality in the classification of mixture data and to understand the impact of its breakdown, we specify conditions for Gaussian universality and discuss their implications for the choice of loss function.
Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Series
Authors: Byoungwoo Park, Hyungi Lee, Juho Lee
Date: 2024-10-08 00:00:00
Tasks: Computational Efficiency, Irregular Time Series, Representation Learning, Time Series, Variational Inference

Many real-world datasets, such as healthcare, climate, and economics, are often collected as irregular time series, which poses challenges for accurate modeling. In this paper, we propose the Amortized Control of continuous State Space Model (ACSSM) for continuous dynamical modeling of time series for irregular and discrete observations. We first present a multi-marginal Doob's $h$-transform to construct a continuous dynamical system conditioned on these irregular observations. Following this, we introduce a variational inference algorithm with a tight evidence lower bound (ELBO), leveraging stochastic optimal control (SOC) theory to approximate the intractable Doob's $h$-transform and simulate the conditioned dynamics. To improve efficiency and scalability during both training and inference, ACSSM employs amortized inference to decouple representation learning from the latent dynamics. Additionally, it incorporates a simulation-free latent dynamics framework and a transformer-based data assimilation scheme, facilitating parallel inference of the latent states and ELBO computation. Through empirical evaluations across a variety of real-world datasets, ACSSM demonstrates superior performance in tasks such as classification, regression, interpolation, and extrapolation, while maintaining computational efficiency.
Optimal Adaptive Experimental Design for Estimating Treatment Effect
Authors: Jiachun Li, David Simchi-Levi, Yunxiao Zhao
Date: 2024-10-07 00:00:00
Tasks: Experimental Design

Given n experiment subjects with potentially heterogeneous covariates and two possible treatments, namely active treatment and control, this paper addresses the fundamental question of determining the optimal accuracy in estimating the treatment effect. Furthermore, we propose an experimental design that approaches this optimal accuracy, giving a (non-asymptotic) answer to this fundamental yet still open question. The methodological contribution is listed as following. First, we establish an idealized optimal estimator with minimal variance as benchmark, and then demonstrate that adaptive experiment is necessary to achieve near-optimal estimation accuracy. Secondly, by incorporating the concept of doubly robust method into sequential experimental design, we frame the optimal estimation problem as an online bandit learning problem, bridging the two fields of statistical estimation and bandit learning. Using tools and ideas from both bandit algorithm design and adaptive statistical estimation, we propose a general low switching adaptive experiment framework, which could be a generic research paradigm for a wide range of adaptive experimental design. Through novel lower bound techniques for non-i.i.d. data, we demonstrate the optimality of our proposed experiment. Numerical result indicates that the estimation accuracy approaches optimal with as few as two or three policy updates.
Scalable Inference for Bayesian Multinomial Logistic-Normal Dynamic Linear Models
Authors: Manan Saxena, Tinghua Chen, Justin D. Silverman
Date: 2024-10-07 00:00:00
Tasks: State Estimation

Many scientific fields collect longitudinal count compositional data. Each observation is a multivariate count vector, where the total counts are arbitrary, and the information lies in the relative frequency of the counts. Multiple authors have proposed Bayesian Multinomial Logistic-Normal Dynamic Linear Models (MLN-DLMs) as a flexible approach to modeling these data. However, adoption of these methods has been limited by computational challenges. This article develops an efficient and accurate approach to posterior state estimation, called $\textit{Fenrir}$. Our approach relies on a novel algorithm for MAP estimation and an accurate approximation to a key posterior marginal of the model. As there are no equivalent methods against which we can compare, we also develop an optimized Stan implementation of MLN-DLMs. Our experiments suggest that Fenrir can be three orders of magnitude more efficient than Stan and can even be incorporated into larger sampling schemes for joint inference of model hyperparameters. Our methods are made available to the community as a user-friendly software library written in C++ with an R interface.
DOPL: Direct Online Preference Learning for Restless Bandits with Preference Feedback
Authors: Guojun Xiong, Ujwal Dinesha, Debajoy Mukherjee, Jian Li, Srinivas Shakkottai
Date: 2024-10-07 00:00:00
Tasks: Multi-Armed Bandits, Sequential Decision Making

Restless multi-armed bandits (RMAB) has been widely used to model constrained sequential decision making problems, where the state of each restless arm evolves according to a Markov chain and each state transition generates a scalar reward. However, the success of RMAB crucially relies on the availability and quality of reward signals. Unfortunately, specifying an exact reward function in practice can be challenging and even infeasible. In this paper, we introduce Pref-RMAB, a new RMAB model in the presence of preference signals, where the decision maker only observes pairwise preference feedback rather than scalar reward from the activated arms at each decision epoch. Preference feedback, however, arguably contains less information than the scalar reward, which makes Pref-RMAB seemingly more difficult. To address this challenge, we present a direct online preference learning (DOPL) algorithm for Pref-RMAB to efficiently explore the unknown environments, adaptively collect preference data in an online manner, and directly leverage the preference feedback for decision-makings. We prove that DOPL yields a sublinear regret. To our best knowledge, this is the first algorithm to ensure $\tilde{\mathcal{O}}(\sqrt{T\ln T})$ regret for RMAB with preference feedback. Experimental results further demonstrate the effectiveness of DOPL.
Deep Learning Methods for S Shaped Utility Maximisation with a Random Reference Point
Authors: Ashley Davey, Harry Zheng
Date: 2024-10-07 00:00:00
Tasks: Deep Learning

We consider the portfolio optimisation problem where the terminal function is an S-shaped utility applied at the difference between the wealth and a random benchmark process. We develop several numerical methods for solving the problem using deep learning and duality methods. We use deep learning methods to solve the associated Hamilton-Jacobi-Bellman equation for both the primal and dual problems, and the adjoint equation arising from the stochastic maximum principle. We compare the solution of this non-concave problem to that of concavified utility, a random function depending on the benchmark, in both complete and incomplete markets. We give some numerical results for power and log utilities to show the accuracy of the suggested algorithms.
Testing Credibility of Public and Private Surveys through the Lens of Regression
Authors: Debabrota Basu, Sourav Chakraborty, Debarshi Chanda, Buddha Dev Das, Arijit Ghosh, Arnab Ray
Date: 2024-10-07 00:00:00
Tasks: regression, Survey

Testing whether a sample survey is a credible representation of the population is an important question to ensure the validity of any downstream research. While this problem, in general, does not have an efficient solution, one might take a task-based approach and aim to understand whether a certain data analysis tool, like linear regression, would yield similar answers both on the population and the sample survey. In this paper, we design an algorithm to test the credibility of a sample survey in terms of linear regression. In other words, we design an algorithm that can certify if a sample survey is good enough to guarantee the correctness of data analysis done using linear regression tools. Nowadays, one is naturally concerned about data privacy in surveys. Thus, we further test the credibility of surveys published in a differentially private manner. Specifically, we focus on Local Differential Privacy (LDP), which is a standard technique to ensure privacy in surveys where the survey participants might not trust the aggregator. We extend our algorithm to work even when the data analysis has been done using surveys with LDP. In the process, we also propose an algorithm that learns with high probability the guarantees a linear regression model on a survey published with LDP. Our algorithm also serves as a mechanism to learn linear regression models from data corrupted with noise coming from any subexponential distribution. We prove that it achieves the optimal estimation error bound for $\ell_1$ linear regression, which might be of broader interest. We prove the theoretical correctness of our algorithms while trying to reduce the sample complexity for both public and private surveys. We also numerically demonstrate the performance of our algorithms on real and synthetic datasets.
Meta-Dynamical State Space Models for Integrative Neural Data Analysis
Authors: Ayesha Vermani, Josue Nassar, Hyungju Jeon, Matthew Dowling, Il Memming Park
Date: 2024-10-07 00:00:00
Tasks: Meta-Learning, State Space Models

Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel settings. However, there has been limited work exploiting the shared structure in neural activity during similar tasks for learning latent dynamics from neural recordings. Existing approaches are designed to infer dynamics from a single dataset and cannot be readily adapted to account for statistical heterogeneities across recordings. In this work, we hypothesize that similar tasks admit a corresponding family of related solutions and propose a novel approach for meta-learning this solution space from task-related neural activity of trained animals. Specifically, we capture the variabilities across recordings on a low-dimensional manifold which concisely parametrizes this family of dynamics, thereby facilitating rapid learning of latent dynamics given new recordings. We demonstrate the efficacy of our approach on few-shot reconstruction and forecasting of synthetic dynamical systems, and neural recordings from the motor cortex during different arm reaching tasks.
Online scalable Gaussian processes with conformal prediction for guaranteed coverage
Authors: Jinwen Xu, Qin Lu, Georgios B. Giannakis
Date: 2024-10-07 00:00:00
Tasks: Conformal Prediction, Gaussian Processes, Prediction, Uncertainty Quantification, valid

The Gaussian process (GP) is a Bayesian nonparametric paradigm that is widely adopted for uncertainty quantification (UQ) in a number of safety-critical applications, including robotics, healthcare, as well as surveillance. The consistency of the resulting uncertainty values however, hinges on the premise that the learning function conforms to the properties specified by the GP model, such as smoothness, periodicity and more, which may not be satisfied in practice, especially with data arriving on the fly. To combat against such model mis-specification, we propose to wed the GP with the prevailing conformal prediction (CP), a distribution-free post-processing framework that produces it prediction sets with a provably valid coverage under the sole assumption of data exchangeability. However, this assumption is usually violated in the online setting, where a prediction set is sought before revealing the true label. To ensure long-term coverage guarantee, we will adaptively set the key threshold parameter based on the feedback whether the true label falls inside the prediction set. Numerical results demonstrate the merits of the online GP-CP approach relative to existing alternatives in the long-term coverage performance.
Thompson Sampling For Combinatorial Bandits: Polynomial Regret and Mismatched Sampling Paradox
Authors: Raymond Zhang, Richard Combes
Date: 2024-10-07 00:00:00
Tasks: Thompson Sampling

We consider Thompson Sampling (TS) for linear combinatorial semi-bandits and subgaussian rewards. We propose the first known TS whose finite-time regret does not scale exponentially with the dimension of the problem. We further show the "mismatched sampling paradox": A learner who knows the rewards distributions and samples from the correct posterior distribution can perform exponentially worse than a learner who does not know the rewards and simply samples from a well-chosen Gaussian posterior. The code used to generate the experiments is available at https://github.com/RaymZhang/CTS-Mismatched-Paradox
A Functional Extension of Semi-Structured Networks
Authors: David Rügamer, Bernard X. W. Liew, Zainab Altai, Almond Stöcker
Date: 2024-10-07 00:00:00
Tasks: Additive models

Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A significant challenge in this integration is maintaining the interpretability of the additive model component. Inspired by large-scale biomechanics datasets, this paper explores extending SSNs to functional data. Existing methods in functional data analysis are promising but often not expressive enough to account for all interactions and non-linearities and do not scale well to large datasets. Although the SSN approach presents a compelling potential solution, its adaptation to functional data remains complex. In this work, we propose a functional SSN method that retains the advantageous properties of classical functional regression approaches while also improving scalability. Our numerical experiments demonstrate that this approach accurately recovers underlying signals, enhances predictive performance, and performs favorably compared to competing methods.
GRU-D Characterizes Age-Specific Temporal Missingness in MIMIC-IV
Authors: Niklas Giesa, Mert Akgül, Sebastian Daniel Boie, Felix Balzer
Date: 2024-10-07 00:00:00
Tasks: Binary Classification, Time Series

Temporal missingness, defined as unobserved patterns in time series, and its predictive potentials represent an emerging area in clinical machine learning. We trained a gated recurrent unit with decay mechanisms, called GRU-D, for a binary classification between elderly - and young patients. We extracted time series for 5 vital signs from MIMIC-IV as model inputs. GRU-D was evaluated with means of 0.780 AUROC and 0.810 AUPRC on bootstrapped data. Interpreting trained model parameters, we found differences in blood pressure missingness and respiratory rate missingness as important predictors learned by parameterized hidden gated units. We successfully showed how GRU-D can be used to reveal patterns in temporal missingness building the basis of novel research directions.
Exploiting Distribution Constraints for Scalable and Efficient Image Retrieval
Authors: Mohammad Omama, Po-han Li, Sandeep P. Chinchali
Date: 2024-10-09 00:00:00
Tasks: Image Retrieval, Retrieval

Image retrieval is crucial in robotics and computer vision, with downstream applications in robot place recognition and vision-based product recommendations. Modern retrieval systems face two key challenges: scalability and efficiency. State-of-the-art image retrieval systems train specific neural networks for each dataset, an approach that lacks scalability. Furthermore, since retrieval speed is directly proportional to embedding size, existing systems that use large embeddings lack efficiency. To tackle scalability, recent works propose using off-the-shelf foundation models. However, these models, though applicable across datasets, fall short in achieving performance comparable to that of dataset-specific models. Our key observation is that, while foundation models capture necessary subtleties for effective retrieval, the underlying distribution of their embedding space can negatively impact cosine similarity searches. We introduce Autoencoders with Strong Variance Constraints (AE-SVC), which, when used for projection, significantly improves the performance of foundation models. We provide an in-depth theoretical analysis of AE-SVC. Addressing efficiency, we introduce Single-shot Similarity Space Distillation ((SS)$_2$D), a novel approach to learn embeddings with adaptive sizes that offers a better trade-off between size and performance. We conducted extensive experiments on four retrieval datasets, including Stanford Online Products (SoP) and Pittsburgh30k, using four different off-the-shelf foundation models, including DinoV2 and CLIP. AE-SVC demonstrates up to a $16\%$ improvement in retrieval performance, while (SS)$_2$D shows a further $10\%$ improvement for smaller embedding sizes.
An Overview of zbMATH Open Digital Library
Authors: Madhurima Deb, Isabel Beckenbach, Matteo Petrera, Dariush Ehsani, Marcel Fuhrmann, Yun Hao, Olaf Teschke, Moritz Schubotz
Date: 2024-10-09 00:00:00
Tasks: Information Retrieval, Retrieval

Mathematical research thrives on the effective dissemination and discovery of knowledge. zbMATH Open has emerged as a pivotal platform in this landscape, offering a comprehensive repository of mathematical literature. Beyond indexing and abstracting, it serves as a unified quality-assured infrastructure for finding, evaluating, and connecting mathematical information that advances mathematical research as well as interdisciplinary exploration. zbMATH Open enables scientific quality control by post-publication reviews and promotes connections between researchers, institutions, and research outputs. This paper represents the functionalities of the most significant features of this open-access service, highlighting its role in shaping the future of mathematical information retrieval.
Performance Evaluation in Multimedia Retrieval
Authors: Loris Sauter, Ralph Gasser, Heiko Schuldt, Abraham Bernstein, Luca Rossetto
Date: 2024-10-09 00:00:00
Tasks: Information Retrieval, Retrieval

Performance evaluation in multimedia retrieval, as in the information retrieval domain at large, relies heavily on retrieval experiments, employing a broad range of techniques and metrics. These can involve human-in-the-loop and machine-only settings for the retrieval process itself and the subsequent verification of results. Such experiments can be elaborate and use-case-specific, which can make them difficult to compare or replicate. In this paper, we present a formal model to express all relevant aspects of such retrieval experiments, as well as a flexible open-source evaluation infrastructure that implements the model. These contributions intend to make a step towards lowering the hurdles for conducting retrieval experiments and improving their reproducibility.