pwc-archive/papers-with-abstracts huggingface dataset:
One Representative-Shot Learning Using a Population-Driven Template with Application to Brain Connectivity Classification and Evolution Prediction
Authors: Umut Guvercin, Mohammed Amine Gharsallaoui, Islem Rekik
Date: 2021-10-06 00:00:00
Tasks: Few-Shot Learning, One-Shot Learning

Few-shot learning presents a challenging paradigm for training discriminative models on a few training samples representing the target classes to discriminate. However, classification methods based on deep learning are ill-suited for such learning as they need large amounts of training data --let alone one-shot learning. Recently, graph neural networks (GNNs) have been introduced to the field of network neuroscience, where the brain connectivity is encoded in a graph. However, with scarce neuroimaging datasets particularly for rare diseases and low-resource clinical facilities, such data-devouring architectures might fail in learning the target task. In this paper, we take a very different approach in training GNNs, where we aim to learn with one sample and achieve the best performance --a formidable challenge to tackle. Specifically, we present the first one-shot paradigm where a GNN is trained on a single population-driven template --namely a connectional brain template (CBT). A CBT is a compact representation of a population of brain graphs capturing the unique connectivity patterns shared across individuals. It is analogous to brain image atlases for neuroimaging datasets. Using a one-representative CBT as a training sample, we alleviate the training load of GNN models while boosting their performance across a variety of classification and regression tasks. We demonstrate that our method significantly outperformed benchmark one-shot learning methods with downstream classification and time-dependent brain graph data forecasting tasks while competing with the train-on-all conventional training strategy. Our source code can be found at https://github.com/basiralab/one-representative-shot-learning.
Likelihood Training of Schrödinger Bridge using Forward-Backward SDEs Theory
Authors: Tianrong Chen, Guan-Horng Liu, Evangelos A. Theodorou
Date: 2021-10-21 00:00:00
Proceeding: ICLR 2022 4
Tasks: Image Generation

Schr\"odinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). However, it remains unclear whether the optimization principle of SB relates to the modern training of deep generative models, which often rely on constructing log-likelihood objectives.This raises questions on the suitability of SB models as a principled alternative for generative applications. In this work, we present a novel computational framework for likelihood training of SB models grounded on Forward-Backward Stochastic Differential Equations Theory - a mathematical methodology appeared in stochastic optimal control that transforms the optimality condition of SB into a set of SDEs. Crucially, these SDEs can be used to construct the likelihood objectives for SB that, surprisingly, generalizes the ones for SGM as special cases. This leads to a new optimization principle that inherits the same SB optimality yet without losing applications of modern generative training techniques, and we show that the resulting training algorithm achieves comparable results on generating realistic images on MNIST, CelebA, and CIFAR10. Our code is available at https://github.com/ghliu/SB-FBSDE.
Analyzing and Improving the Optimization Landscape of Noise-Contrastive Estimation
Authors: Bingbin Liu, Elan Rosenfeld, Pradeep Ravikumar, Andrej Risteski
Date: 2021-10-21 00:00:00
Proceeding: ICLR 2022 4

Noise-contrastive estimation (NCE) is a statistically consistent method for learning unnormalized probabilistic models. It has been empirically observed that the choice of the noise distribution is crucial for NCE's performance. However, such observations have never been made formal or quantitative. In fact, it is not even clear whether the difficulties arising from a poorly chosen noise distribution are statistical or algorithmic in nature. In this work, we formally pinpoint reasons for NCE's poor performance when an inappropriate noise distribution is used. Namely, we prove these challenges arise due to an ill-behaved (more precisely, flat) loss landscape. To address this, we introduce a variant of NCE called "eNCE" which uses an exponential loss and for which normalized gradient descent addresses the landscape issues provably when the target and noise distributions are in a given exponential family.
On Optimal Interpolation In Linear Regression
Authors: Eduard Oravkin, Patrick Rebeschini
Date: 2021-10-21 00:00:00
Proceeding: NeurIPS 2021 12
Tasks: Learning Theory, regression

Understanding when and why interpolating methods generalize well has recently been a topic of interest in statistical learning theory. However, systematically connecting interpolating methods to achievable notions of optimality has only received partial attention. In this paper, we investigate the question of what is the optimal way to interpolate in linear regression using functions that are linear in the response variable (as the case for the Bayes optimal estimator in ridge regression) and depend on the data, the population covariance of the data, the signal-to-noise ratio and the covariance of the prior for the signal, but do not depend on the value of the signal itself nor the noise vector in the training data. We provide a closed-form expression for the interpolator that achieves this notion of optimality and show that it can be derived as the limit of preconditioned gradient descent with a specific initialization. We identify a regime where the minimum-norm interpolator provably generalizes arbitrarily worse than the optimal response-linear achievable interpolator that we introduce, and validate with numerical experiments that the notion of optimality we consider can be achieved by interpolating methods that only use the training data as input in the case of an isotropic prior. Finally, we extend the notion of optimal response-linear interpolation to random features regression under a linear data-generating model that has been previously studied in the literature.
User-friendly introduction to PAC-Bayes bounds
Authors: Pierre Alquier
Date: 2021-10-21 00:00:00
Tasks: Learning Theory

Aggregated predictors are obtained by making a set of basic predictors vote according to some weights, that is, to some probability distribution. Randomized predictors are obtained by sampling in a set of basic predictors, according to some prescribed probability distribution. Thus, aggregated and randomized predictors have in common that they are not defined by a minimization problem, but by a probability distribution on the set of predictors. In statistical learning theory, there is a set of tools designed to understand the generalization ability of such procedures: PAC-Bayesian or PAC-Bayes bounds. Since the original PAC-Bayes bounds of D. McAllester, these tools have been considerably improved in many directions (we will for example describe a simplified version of the localization technique of O. Catoni that was missed by the community, and later rediscovered as "mutual information bounds"). Very recently, PAC-Bayes bounds received a considerable attention: for example there was workshop on PAC-Bayes at NIPS 2017, "(Almost) 50 Shades of Bayesian Learning: PAC-Bayesian trends and insights", organized by B. Guedj, F. Bach and P. Germain. One of the reason of this recent success is the successful application of these bounds to neural networks by G. Dziugaite and D. Roy. An elementary introduction to PAC-Bayes theory is still missing. This is an attempt to provide such an introduction.
Sensing Cox Processes via Posterior Sampling and Positive Bases
Authors: Mojmír Mutný, Andreas Krause
Date: 2021-10-21 00:00:00
Tasks: Experimental Design, Point Processes

We study adaptive sensing of Cox point processes, a widely used model from spatial statistics. We introduce three tasks: maximization of captured events, search for the maximum of the intensity function and learning level sets of the intensity function. We model the intensity function as a sample from a truncated Gaussian process, represented in a specially constructed positive basis. In this basis, the positivity constraint on the intensity function has a simple form. We show how an minimal description positive basis can be adapted to the covariance kernel, non-stationarity and make connections to common positive bases from prior works. Our adaptive sensing algorithms use Langevin dynamics and are based on posterior sampling (\textsc{Cox-Thompson}) and top-two posterior sampling (\textsc{Top2}) principles. With latter, the difference between samples serves as a surrogate to the uncertainty. We demonstrate the approach using examples from environmental monitoring and crime rate modeling, and compare it to the classical Bayesian experimental design approach.
DMS, AE, DAA: methods and applications of adaptive time series model selection, ensemble, and financial evaluation
Authors: Parley Ruogu Yang, Ryan Lucas
Date: 2021-10-21 00:00:00
Tasks: Model Selection, Time Series, Time Series Analysis

We introduce three adaptive time series learning methods, called Dynamic Model Selection (DMS), Adaptive Ensemble (AE), and Dynamic Asset Allocation (DAA). The methods respectively handle model selection, ensembling, and contextual evaluation in financial time series. Empirically, we use the methods to forecast the returns of four key indices in the US market, incorporating information from the VIX and Yield curves. We present financial applications of the learning results, including fully-automated portfolios and dynamic hedging strategies. The strategies strongly outperform long-only benchmarks over our testing period, spanning from Q4 2015 to the end of 2021. The key outputs of the learning methods are interpreted during the 2020 market crash.
Statistical Finite Elements via Langevin Dynamics
Authors: Ömer Deniz Akyildiz, Connor Duffin, Sotirios Sabanis, Mark Girolami
Date: 2021-10-21 00:00:00
Tasks: Uncertainty Quantification

The recent statistical finite element method (statFEM) provides a coherent statistical framework to synthesise finite element models with observed data. Through embedding uncertainty inside of the governing equations, finite element solutions are updated to give a posterior distribution which quantifies all sources of uncertainty associated with the model. However to incorporate all sources of uncertainty, one must integrate over the uncertainty associated with the model parameters, the known forward problem of uncertainty quantification. In this paper, we make use of Langevin dynamics to solve the statFEM forward problem, studying the utility of the unadjusted Langevin algorithm (ULA), a Metropolis-free Markov chain Monte Carlo sampler, to build a sample-based characterisation of this otherwise intractable measure. Due to the structure of the statFEM problem, these methods are able to solve the forward problem without explicit full PDE solves, requiring only sparse matrix-vector products. ULA is also gradient-based, and hence provides a scalable approach up to high degrees-of-freedom. Leveraging the theory behind Langevin-based samplers, we provide theoretical guarantees on sampler performance, demonstrating convergence, for both the prior and posterior, in the Kullback-Leibler divergence, and, in Wasserstein-2, with further results on the effect of preconditioning. Numerical experiments are also provided, for both the prior and posterior, to demonstrate the efficacy of the sampler, with a Python package also included.
Inverse Optimal Control Adapted to the Noise Characteristics of the Human Sensorimotor System
Authors: Matthias Schultheis, Dominik Straub, Constantin A. Rothkopf
Date: 2021-10-21 00:00:00
Proceeding: NeurIPS 2021 12
Tasks: Descriptive

Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for a task and the optimality of human behavior is evaluated by comparing observed and predicted trajectories. Here, we introduce inverse optimal control with signal-dependent noise, which allows inferring the cost function from observed behavior. To do so, we formalize the problem as a partially observable Markov decision process and distinguish between the agent's and the experimenter's inference problems. Specifically, we derive a probabilistic formulation of the evolution of states and belief states and an approximation to the propagation equation in the linear-quadratic Gaussian problem with signal-dependent noise. We extend the model to the case of partial observability of state variables from the point of view of the experimenter. We show the feasibility of the approach through validation on synthetic data and application to experimental data. Our approach enables recovering the costs and benefits implicit in human sequential sensorimotor behavior, thereby reconciling normative and descriptive approaches in a computational framework.
Bayesian Meta-Learning Through Variational Gaussian Processes
Authors: Vivek Myers, Nikhil Sardana
Date: 2021-10-21 00:00:00
Tasks: Gaussian Processes, Meta-Learning

Recent advances in the field of meta-learning have tackled domains consisting of large numbers of small ("few-shot") supervised learning tasks. Meta-learning algorithms must be able to rapidly adapt to any individual few-shot task, fitting to a small support set within a task and using it to predict the labels of the task's query set. This problem setting can be extended to the Bayesian context, wherein rather than predicting a single label for each query data point, a model predicts a distribution of labels capturing its uncertainty. Successful methods in this domain include Bayesian ensembling of MAML-based models, Bayesian neural networks, and Gaussian processes with learned deep kernel and mean functions. While Gaussian processes have a robust Bayesian interpretation in the meta-learning context, they do not naturally model non-Gaussian predictive posteriors for expressing uncertainty. In this paper, we design a theoretically principled method, VMGP, extending Gaussian-process-based meta-learning to allow for high-quality, arbitrary non-Gaussian uncertainty predictions. On benchmark environments with complex non-smooth or discontinuous structure, we find our VMGP method performs significantly better than existing Bayesian meta-learning baselines.
Mean Nyström Embeddings for Adaptive Compressive Learning
Authors: Antoine Chatalic, Luigi Carratino, Ernesto de Vito, Lorenzo Rosasco
Date: 2021-10-21 00:00:00

Compressive learning is an approach to efficient large scale learning based on sketching an entire dataset to a single mean embedding (the sketch), i.e. a vector of generalized moments. The learning task is then approximately solved as an inverse problem using an adapted parametric model. Previous works in this context have focused on sketches obtained by averaging random features, that while universal can be poorly adapted to the problem at hand. In this paper, we propose and study the idea of performing sketching based on data-dependent Nystr\"om approximation. From a theoretical perspective we prove that the excess risk can be controlled under a geometric assumption relating the parametric model used to learn from the sketch and the covariance operator associated to the task at hand. Empirically, we show for k-means clustering and Gaussian modeling that for a fixed sketch size, Nystr\"om sketches indeed outperform those built with random features.
Efficient Gradient Flows in Sliced-Wasserstein Space
Authors: Clément Bonet, Nicolas Courty, François Septier, Lucas Drumetz
Date: 2021-10-21 00:00:00
Tasks: Bayesian Inference, Image Generation

Minimizing functionals in the space of probability distributions can be done with Wasserstein gradient flows. To solve them numerically, a possible approach is to rely on the Jordan-Kinderlehrer-Otto (JKO) scheme which is analogous to the proximal scheme in Euclidean spaces. However, it requires solving a nested optimization problem at each iteration, and is known for its computational challenges, especially in high dimension. To alleviate it, very recent works propose to approximate the JKO scheme leveraging Brenier's theorem, and using gradients of Input Convex Neural Networks to parameterize the density (JKO-ICNN). However, this method comes with a high computational cost and stability issues. Instead, this work proposes to use gradient flows in the space of probability measures endowed with the sliced-Wasserstein (SW) distance. We argue that this method is more flexible than JKO-ICNN, since SW enjoys a closed-form differentiable approximation. Thus, the density at each step can be parameterized by any generative model which alleviates the computational burden and makes it tractable in higher dimensions.
Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox
Authors: Yifan Cui
Date: 2021-10-21 00:00:00
Tasks: Causal Inference, Decision Making

Unmeasured confounding is a threat to causal inference and gives rise to biased estimates. In this article, we consider the problem of individualized decision-making under partial identification. Firstly, we argue that when faced with unmeasured confounding, one should pursue individualized decision-making using partial identification in a comprehensive manner. We establish a formal link between individualized decision-making under partial identification and classical decision theory by considering a lower bound perspective of value/utility function. Secondly, building on this unified framework, we provide a novel minimax solution (i.e., a rule that minimizes the maximum regret for so-called opportunists) for individualized decision-making/policy assignment. Lastly, we provide an interesting paradox drawing on novel connections between two challenging domains, that is, individualized decision-making and unmeasured confounding. Although motivated by instrumental variable bounds, we emphasize that the general framework proposed in this article would in principle apply for a rich set of bounds that might be available under partial identification.
Data splitting improves statistical performance in overparametrized regimes
Authors: Nicole Mücke, Enrico Reiss, Jonas Rungenhagen, Markus Klein
Date: 2021-10-21 00:00:00
Tasks: regression

While large training datasets generally offer improvement in model performance, the training process becomes computationally expensive and time consuming. Distributed learning is a common strategy to reduce the overall training time by exploiting multiple computing devices. Recently, it has been observed in the single machine setting that overparametrization is essential for benign overfitting in ridgeless regression in Hilbert spaces. We show that in this regime, data splitting has a regularizing effect, hence improving statistical performance and computational complexity at the same time. We further provide a unified framework that allows to analyze both the finite and infinite dimensional setting. We numerically demonstrate the effect of different model parameters.
$\ell_{\infty}$-Bounds of the MLE in the BTL Model under General Comparison Graphs
Authors: Wanshan Li, Shamindra Shrotriya, Alessandro Rinaldo
Date: 2021-10-20 00:00:00

The Bradley-Terry-Luce (BTL) model is a popular statistical approach for estimating the global ranking of a collection of items using pairwise comparisons. To ensure accurate ranking, it is essential to obtain precise estimates of the model parameters in the $\ell_{\infty}$-loss. The difficulty of this task depends crucially on the topology of the pairwise comparison graph over the given items. However, beyond very few well-studied cases, such as the complete and Erd\"os-R\'enyi comparison graphs, little is known about the performance of the maximum likelihood estimator MLE) of the BTL model parameters in the $\ell_{\infty}$-loss under more general graph topologies. In this paper, we derive novel, general upper bounds on the $\ell_{\infty}$ estimation error of the BTL MLE that depend explicitly on the algebraic connectivity of the comparison graph, the maximal performance gap across items and the sample complexity. We demonstrate that the derived bounds perform well and in some cases are sharper compared to known results obtained using different loss functions and more restricted assumptions and graph topologies. We carefully compare our results to Yan et al. (2012), which is closest in spirit to our work. We further provide minimax lower bounds under $\ell_{\infty}$-error that nearly match the upper bounds over a class of sufficiently regular graph topologies. Finally, we study the implications of our $\ell_{\infty}$-bounds for efficient (offline) tournament design. We illustrate and discuss our findings through various examples and simulations.
Estimating Optimal Infinite Horizon Dynamic Treatment Regimes via pT-Learning
Authors: Wenzhuo Zhou, Ruoqing Zhu, Annie Qu
Date: 2021-10-20 00:00:00
Tasks: Decision Making

Recent advances in mobile health (mHealth) technology provide an effective way to monitor individuals' health statuses and deliver just-in-time personalized interventions. However, the practical use of mHealth technology raises unique challenges to existing methodologies on learning an optimal dynamic treatment regime. Many mHealth applications involve decision-making with large numbers of intervention options and under an infinite time horizon setting where the number of decision stages diverges to infinity. In addition, temporary medication shortages may cause optimal treatments to be unavailable, while it is unclear what alternatives can be used. To address these challenges, we propose a Proximal Temporal consistency Learning (pT-Learning) framework to estimate an optimal regime that is adaptively adjusted between deterministic and stochastic sparse policy models. The resulting minimax estimator avoids the double sampling issue in the existing algorithms. It can be further simplified and can easily incorporate off-policy data without mismatched distribution corrections. We study theoretical properties of the sparse policy and establish finite-sample bounds on the excess risk and performance error. The proposed method is provided in our proximalDTR package and is evaluated through extensive simulation studies and the OhioT1DM mHealth dataset.
Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry
Authors: Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao
Date: 2021-10-20 00:00:00
Tasks: Riemannian optimization

Learning with symmetric positive definite (SPD) matrices has many applications in machine learning. Consequently, understanding the Riemannian geometry of SPD matrices has attracted much attention lately. A particular Riemannian geometry of interest is the recently proposed Bures-Wasserstein (BW) geometry which builds on the Wasserstein distance between the Gaussian densities. In this paper, we propose a novel generalization of the BW geometry, which we call the GBW geometry. The proposed generalization is parameterized by a symmetric positive definite matrix $\mathbf{M}$ such that when $\mathbf{M} = \mathbf{I}$, we recover the BW geometry. We provide a rigorous treatment to study various differential geometric notions on the proposed novel generalized geometry which makes it amenable to various machine learning applications. We also present experiments that illustrate the efficacy of the proposed GBW geometry over the BW geometry.