pwc-archive/papers-with-abstracts huggingface dataset:
Orlicz regrets to consistently bound statistics of random variables with an application to environmental indicators
Authors: Hidekazu Yoshioka, Yumi Yoshioka
Date: 2023-10-08 00:00:00
Tasks: Management

Evaluating environmental variables that vary stochastically is the principal topic for designing better environmental management and restoration schemes. Both the upper and lower estimates of these variables, such as water quality indices and flood and drought water levels, are important and should be consistently evaluated within a unified mathematical framework. We propose a novel pair of Orlicz regrets to consistently bound the statistics of random variables both from below and above. Here, consistency indicates that the upper and lower bounds are evaluated with common coefficients and parameter values being different from some of the risk measures proposed thus far. Orlicz regrets can flexibly evaluate the statistics of random variables based on their tail behavior. The explicit linkage between Orlicz regrets and divergence risk measures was exploited to better comprehend them. We obtain sufficient conditions to pose the Orlicz regrets as well as divergence risk measures, and further provide gradient descent-type numerical algorithms to compute them. Finally, we apply the proposed mathematical framework to the statistical evaluation of 31-year water quality data as key environmental indicators in a Japanese river environment.
A Corrected Expected Improvement Acquisition Function Under Noisy Observations
Authors: Han Zhou, Xingchen Ma, Matthew B Blaschko
Date: 2023-10-08 00:00:00
Tasks: Bayesian Optimization, Model Compression

Sequential maximization of expected improvement (EI) is one of the most widely used policies in Bayesian optimization because of its simplicity and ability to handle noisy observations. In particular, the improvement function often uses the best posterior mean as the best incumbent in noisy settings. However, the uncertainty associated with the incumbent solution is often neglected in many analytic EI-type methods: a closed-form acquisition function is derived in the noise-free setting, but then applied to the setting with noisy observations. To address this limitation, we propose a modification of EI that corrects its closed-form expression by incorporating the covariance information provided by the Gaussian Process (GP) model. This acquisition function specializes to the classical noise-free result, and we argue should replace that formula in Bayesian optimization software packages, tutorials, and textbooks. This enhanced acquisition provides good generality for noisy and noiseless settings. We show that our method achieves a sublinear convergence rate on the cumulative regret bound under heteroscedastic observation noise. Our empirical results demonstrate that our proposed acquisition function can outperform EI in the presence of noisy observations on benchmark functions for black-box optimization, as well as on parameter search for neural network model compression.
Compressed online Sinkhorn
Authors: Fengpei Wang, Clarice Poon, Tony Shardlow
Date: 2023-10-08 00:00:00

The use of optimal transport (OT) distances, and in particular entropic-regularised OT distances, is an increasingly popular evaluation metric in many areas of machine learning and data science. Their use has largely been driven by the availability of efficient algorithms such as the Sinkhorn algorithm. One of the drawbacks of the Sinkhorn algorithm for large-scale data processing is that it is a two-phase method, where one first draws a large stream of data from the probability distributions, before applying the Sinkhorn algorithm to the discrete probability measures. More recently, there have been several works developing stochastic versions of Sinkhorn that directly handle continuous streams of data. In this work, we revisit the recently introduced online Sinkhorn algorithm of [Mensch and Peyr\'e, 2020]. Our contributions are twofold: We improve the convergence analysis for the online Sinkhorn algorithm, the new rate that we obtain is faster than the previous rate under certain parameter choices. We also present numerical results to verify the sharpness of our result. Secondly, we propose the compressed online Sinkhorn algorithm which combines measure compression techniques with the online Sinkhorn algorithm. We provide numerical experiments to show practical numerical gains, as well as theoretical guarantees on the efficiency of our approach.
Model-adapted Fourier sampling for generative compressed sensing
Authors: Aaron Berk, Simone Brugiapaglia, Yaniv Plan, Matthew Scott, Xia Sheng, Ozgur Yilmaz
Date: 2023-10-08 00:00:00
Tasks: compressed sensing, model

We study generative compressed sensing when the measurement matrix is randomly subsampled from a unitary matrix (with the DFT as an important special case). It was recently shown that $\textit{O}(kdn\| \boldsymbol{\alpha}\|_{\infty}^{2})$ uniformly random Fourier measurements are sufficient to recover signals in the range of a neural network $G:\mathbb{R}^k \to \mathbb{R}^n$ of depth $d$, where each component of the so-called local coherence vector $\boldsymbol{\alpha}$ quantifies the alignment of a corresponding Fourier vector with the range of $G$. We construct a model-adapted sampling strategy with an improved sample complexity of $\textit{O}(kd\| \boldsymbol{\alpha}\|_{2}^{2})$ measurements. This is enabled by: (1) new theoretical recovery guarantees that we develop for nonuniformly random sampling distributions and then (2) optimizing the sampling distribution to minimize the number of measurements needed for these guarantees. This development offers a sample complexity applicable to natural signal classes, which are often almost maximally coherent with low Fourier frequencies. Finally, we consider a surrogate sampling scheme, and validate its performance in recovery experiments using the CelebA dataset.
Robust matrix completion via Novel M-estimator Functions
Authors: Zhi-Yong Wang, Hing Cheung So
Date: 2023-10-08 00:00:00
Tasks: Matrix Completion

M-estmators including the Welsch and Cauchy have been widely adopted for robustness against outliers, but they also down-weigh the uncontaminated data. To address this issue, we devise a framework to generate a class of nonconvex functions which only down-weigh outlier-corrupted observations. Our framework is then applied to the Welsch, Cauchy and $\ell_p$-norm functions to produce the corresponding robust loss functions. Targeting on the application of robust matrix completion, efficient algorithms based on these functions are developed and their convergence is analyzed. Finally, extensive numerical results demonstrate that the proposed methods are superior to the competitors in terms of recovery accuracy and runtime.
The Conditional Prediction Function: A Novel Technique to Control False Discovery Rate for Complex Models
Authors: Yushu Shi, Michael Martens
Date: 2023-10-07 00:00:00
Tasks: Variable Selection

In modern scientific research, the objective is often to identify which variables are associated with an outcome among a large class of potential predictors. This goal can be achieved by selecting variables in a manner that controls the the false discovery rate (FDR), the proportion of irrelevant predictors among the selections. Knockoff filtering is a cutting-edge approach to variable selection that provides FDR control. Existing knockoff statistics frequently employ linear models to assess relationships between features and the response, but the linearity assumption is often violated in real world applications. This may result in poor power to detect truly prognostic variables. We introduce a knockoff statistic based on the conditional prediction function (CPF), which can pair with state-of-art machine learning predictive models, such as deep neural networks. The CPF statistics can capture the nonlinear relationships between predictors and outcomes while also accounting for correlation between features. We illustrate the capability of the CPF statistics to provide superior power over common knockoff statistics with continuous, categorical, and survival outcomes using repeated simulations. Knockoff filtering with the CPF statistics is demonstrated using (1) a residential building dataset to select predictors for the actual sales prices and (2) the TCGA dataset to select genes that are correlated with disease staging in lung cancer patients.
General Graph Random Features
Authors: Isaac Reid, Krzysztof Choromanski, Eli Berger, Adrian Weller
Date: 2023-10-07 00:00:00
Tasks: Node Clustering

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.
Repelling Random Walks
Authors: Isaac Reid, Eli Berger, Krzysztof Choromanski, Adrian Weller
Date: 2023-10-07 00:00:00

We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities are unmodified, we are able to explore the graph more efficiently, improving the concentration of statistical estimators whilst leaving them unbiased. The mechanism has a trivial drop-in implementation. We showcase the effectiveness of repelling random walks in a range of settings including estimation of graph kernels, the PageRank vector and graphlet concentrations. We provide detailed experimental evaluation and robust theoretical guarantees. To our knowledge, repelling random walks constitute the first rigorously studied quasi-Monte Carlo scheme correlating the directions of walkers on a graph, inviting new research in this exciting nascent domain.
Subspace Identification for Multi-Source Domain Adaptation
Authors: Zijian Li, Ruichu Cai, Guangyi Chen, Boyang Sun, Zhifeng Hao, Kun Zhang
Date: 2023-10-07 00:00:00
Proceeding: NeurIPS 2023 11
Tasks: Disentanglement, Domain Adaptation, Variational Inference

Multi-source domain adaptation (MSDA) methods aim to transfer knowledge from multiple labeled source domains to an unlabeled target domain. Although current methods achieve target joint distribution identifiability by enforcing minimal changes across domains, they often necessitate stringent conditions, such as an adequate number of domains, monotonic transformation of latent variables, and invariant label distributions. These requirements are challenging to satisfy in real-world applications. To mitigate the need for these strict assumptions, we propose a subspace identification theory that guarantees the disentanglement of domain-invariant and domain-specific variables under less restrictive constraints regarding domain numbers and transformation properties, thereby facilitating domain adaptation by minimizing the impact of domain shifts on invariant variables. Based on this theory, we develop a Subspace Identification Guarantee (SIG) model that leverages variational inference. Furthermore, the SIG model incorporates class-aware conditional alignment to accommodate target shifts where label distributions change with the domains. Experimental results demonstrate that our SIG model outperforms existing MSDA techniques on various benchmark datasets, highlighting its effectiveness in real-world applications.
Robust Transfer Learning with Unreliable Source Data
Authors: Jianqing Fan, Cheng Gao, Jason M. Klusowski
Date: 2023-10-06 00:00:00
Tasks: regression, Transfer Learning

This paper addresses challenges in robust transfer learning stemming from ambiguity in Bayes classifiers and weak transferable signals between the target and source distribution. We introduce a novel quantity called the ''ambiguity level'' that measures the discrepancy between the target and source regression functions, propose a simple transfer learning procedure, and establish a general theorem that shows how this new quantity is related to the transferability of learning in terms of risk improvements. Our proposed ''Transfer Around Boundary'' (TAB) model, with a threshold balancing the performance of target and source data, is shown to be both efficient and robust, improving classification while avoiding negative transfer. Moreover, we demonstrate the effectiveness of the TAB model on non-parametric classification and logistic regression tasks, achieving upper bounds which are optimal up to logarithmic factors. Simulation studies lend further support to the effectiveness of TAB. We also provide simple approaches to bound the excess misclassification error without the need for specialized knowledge in transfer learning.
A Double Machine Learning Approach for the Evaluation of COVID-19 Vaccine Effectiveness under the Test-Negative Design: Analysis of Québec Administrative Data
Authors: Cong Jiang, Denis Talbot, Sara Carazo, Mireille E Schnitzer
Date: 2023-10-06 00:00:00
Tasks: Selection bias

The test-negative design (TND), which is routinely used for monitoring seasonal flu vaccine effectiveness (VE), has recently become integral to COVID-19 vaccine surveillance, notably in Qu\'ebec, Canada. Some studies have addressed the identifiability and estimation of causal parameters under the TND, but efficiency bounds for nonparametric estimators of the target parameter under the unconfoundedness assumption have not yet been investigated. Motivated by the goal of improving adjustment for measured confounders when estimating COVID-19 VE among community-dwelling people aged $\geq 60$ years in Qu\'ebec, we propose a one-step doubly robust and locally efficient estimator called TNDDR (TND doubly robust), which utilizes cross-fitting (sample splitting) and can incorporate machine learning techniques to estimate the nuisance functions and thus improve control for measured confounders. We derive the efficient influence function (EIF) for the marginal expectation of the outcome under a vaccination intervention, explore the von Mises expansion, and establish the conditions for $\sqrt{n}-$consistency, asymptotic normality and double robustness of TNDDR. The proposed estimator is supported by both theoretical and empirical justifications.
Risk factor aggregation and stress testing
Authors: Natalie Packham
Date: 2023-10-06 00:00:00
Tasks: Dimensionality Reduction

Stress testing refers to the application of adverse financial or macroeconomic scenarios to a portfolio. For this purpose, financial or macroeconomic risk factors are linked with asset returns, typically via a factor model. We expand the range of risk factors by adapting dimension-reduction techniques from unsupervised learning, namely PCA and autoencoders. This results in aggregated risk factors, encompassing a global factor, factors representing broad geographical regions, and factors specific to cyclical and defensive industries. As the adapted PCA and autoencoders provide an interpretation of the latent factors, this methodology is also valuable in other areas where dimension-reduction and explainability are crucial.
Simultaneous Dimensionality Reduction: A Data Efficient Approach for Multimodal Representations Learning
Authors: Eslam Abdelaleem, Ahmed Roman, K. Michael Martini, Ilya Nemenman
Date: 2023-10-05 00:00:00
Tasks: Dimensionality Reduction

We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a paradigmatic example, each modality is compressed independently, striving to retain as much variation within each modality as possible. In contrast, in SDR, one simultaneously compresses the modalities to maximize the covariation between the reduced descriptions while paying less attention to how much individual variation is preserved. Paradigmatic examples include Partial Least Squares and Canonical Correlations Analysis. Even though these DR methods are a staple of statistics, their relative accuracy and data set size requirements are poorly understood. We introduce a generative linear model to synthesize multimodal data with known variance and covariance structures to examine these questions. We assess the accuracy of the reconstruction of the covariance structures as a function of the number of samples, signal-to-noise ratio, and the number of varying and covarying signals in the data. Using numerical experiments, we demonstrate that linear SDR methods consistently outperform linear IDR methods and yield higher-quality, more succinct reduced-dimensional representations with smaller datasets. Remarkably, regularized CCA can identify low-dimensional weak covarying structures even when the number of samples is much smaller than the dimensionality of the data, which is a regime challenging for all dimensionality reduction methods. Our work corroborates and explains previous observations in the literature that SDR can be more effective in detecting covariation patterns in data. These findings suggest that SDR should be preferred to IDR in real-world data analysis when detecting covariation is more important than preserving variation.
ProGO: Probabilistic Global Optimizer
Authors: Xinyu Zhang, Sujit Ghosh
Date: 2023-10-04 00:00:00
Tasks: Bayesian Optimization, global-optimization

In the field of global optimization, many existing algorithms face challenges posed by non-convex target functions and high computational complexity or unavailability of gradient information. These limitations, exacerbated by sensitivity to initial conditions, often lead to suboptimal solutions or failed convergence. This is true even for Metaheuristic algorithms designed to amalgamate different optimization techniques to improve their efficiency and robustness. To address these challenges, we develop a sequence of multidimensional integration-based methods that we show to converge to the global optima under some mild regularity conditions. Our probabilistic approach does not require the use of gradients and is underpinned by a mathematically rigorous convergence framework anchored in the nuanced properties of nascent optima distribution. In order to alleviate the problem of multidimensional integration, we develop a latent slice sampler that enjoys a geometric rate of convergence in generating samples from the nascent optima distribution, which is used to approximate the global optima. The proposed Probabilistic Global Optimizer (ProGO) provides a scalable unified framework to approximate the global optima of any continuous function defined on a domain of arbitrary dimension. Empirical illustrations of ProGO across a variety of popular non-convex test functions (having finite global optima) reveal that the proposed algorithm outperforms, by order of magnitude, many existing state-of-the-art methods, including gradient-based, zeroth-order gradient-free, and some Bayesian Optimization methods, in term regret value and speed of convergence. It is, however, to be noted that our approach may not be suitable for functions that are expensive to compute.
Sequential Tag Recommendation
Authors: Bing Liu, Pengyu Xu, Sijin Lu, Shijing Wang, Hongjian Sun, Liping Jing
Date: 2023-10-09 00:00:00
Tasks: Recommendation Systems, Retrieval, TAG

With the development of Internet technology and the expansion of social networks, online platforms have become an important way for people to obtain information. The introduction of tags facilitates information categorization and retrieval. Meanwhile, the development of tag recommendation systems not only enables users to input tags more efficiently, but also improves the quality of tags. However, current tag recommendation methods only consider the content of the current post and do not take into account the influence of user preferences. Since the main body of tag recommendation is the user, it is very necessary to obtain the user's tagging habits. Therefore, this paper proposes a tag recommendation algorithm (MLP4STR) based on the dynamic preference of user's behavioral sequence, which models the user's historical post information and historical tag information to obtain the user's dynamic interest changes. A pure MLP structure across feature dimensions is used in sequence modeling to model the interaction between tag content and post content to fully extract the user's interests. Finally tag recommendation is performed.
Augmented Embeddings for Custom Retrievals
Authors: Anirudh Khatry, Yasharth Bajpai, Priyanshu Gupta, Sumit Gulwani, Ashish Tiwari
Date: 2023-10-09 00:00:00
Tasks: Information Retrieval, Retrieval

Information retrieval involves selecting artifacts from a corpus that are most relevant to a given search query. The flavor of retrieval typically used in classical applications can be termed as homogeneous and relaxed, where queries and corpus elements are both natural language (NL) utterances (homogeneous) and the goal is to pick most relevant elements from the corpus in the Top-K, where K is large, such as 10, 25, 50 or even 100 (relaxed). Recently, retrieval is being used extensively in preparing prompts for large language models (LLMs) to enable LLMs to perform targeted tasks. These new applications of retrieval are often heterogeneous and strict -- the queries and the corpus contain different kinds of entities, such as NL and code, and there is a need for improving retrieval at Top-K for small values of K, such as K=1 or 3 or 5. Current dense retrieval techniques based on pretrained embeddings provide a general-purpose and powerful approach for retrieval, but they are oblivious to task-specific notions of similarity of heterogeneous artifacts. We introduce Adapted Dense Retrieval, a mechanism to transform embeddings to enable improved task-specific, heterogeneous and strict retrieval. Adapted Dense Retrieval works by learning a low-rank residual adaptation of the pretrained black-box embedding. We empirically validate our approach by showing improvements over the state-of-the-art general-purpose embeddings-based baseline.