pwc-archive/papers-with-abstracts huggingface dataset:
Computationally Efficient Approximations for Matrix-based Renyi's Entropy
Authors: Tieliang Gong, Yuxin Dong, Shujian Yu, Bo Dong
Date: 2021-12-27 00:00:00

The recently developed matrix based Renyi's entropy enables measurement of information in data simply using the eigenspectrum of symmetric positive semi definite (PSD) matrices in reproducing kernel Hilbert space, without estimation of the underlying data distribution. This intriguing property makes the new information measurement widely adopted in multiple statistical inference and learning tasks. However, the computation of such quantity involves the trace operator on a PSD matrix $G$ to power $\alpha$(i.e., $tr(G^\alpha)$), with a normal complexity of nearly $O(n^3)$, which severely hampers its practical usage when the number of samples (i.e., $n$) is large. In this work, we present computationally efficient approximations to this new entropy functional that can reduce its complexity to even significantly less than $O(n^2)$. To this end, we leverage the recent progress on Randomized Numerical Linear Algebra, developing Taylor, Chebyshev and Lanczos approximations to $tr(G^\alpha)$ for arbitrary values of $\alpha$ by converting it into matrix-vector multiplications problem. We also establish the connection between the matrix-based Renyi's entropy and PSD matrix approximation, which enables exploiting both clustering and block low-rank structure of $G$ to further reduce the computational cost. We theoretically provide approximation accuracy guarantees and illustrate the properties of different approximations. Large-scale experimental evaluations on both synthetic and real-world data corroborate our theoretical findings, showing promising speedup with negligible loss in accuracy.
Wasserstein Flow Meets Replicator Dynamics: A Mean-Field Analysis of Representation Learning in Actor-Critic
Authors: Yufeng Zhang, Siyu Chen, Zhuoran Yang, Michael I. Jordan, Zhaoran Wang
Date: 2021-12-27 00:00:00
Proceeding: NeurIPS 2021 12
Tasks: Representation Learning

Actor-critic (AC) algorithms, empowered by neural networks, have had significant empirical success in recent years. However, most of the existing theoretical support for AC algorithms focuses on the case of linear function approximations, or linearized neural networks, where the feature representation is fixed throughout training. Such a limitation fails to capture the key aspect of representation learning in neural AC, which is pivotal in practical problems. In this work, we take a mean-field perspective on the evolution and convergence of feature-based neural AC. Specifically, we consider a version of AC where the actor and critic are represented by overparameterized two-layer neural networks and are updated with two-timescale learning rates. The critic is updated by temporal-difference (TD) learning with a larger stepsize while the actor is updated via proximal policy optimization (PPO) with a smaller stepsize. In the continuous-time and infinite-width limiting regime, when the timescales are properly separated, we prove that neural AC finds the globally optimal policy at a sublinear rate. Additionally, we prove that the feature representation induced by the critic network is allowed to evolve within a neighborhood of the initial one.
AIDA: An Active Inference-based Design Agent for Audio Processing Algorithms
Authors: Albert Podusenko, Bart van Erp, Magnus Koudahl, Bert de Vries
Date: 2021-12-26 00:00:00

In this paper we present AIDA, which is an active inference-based agent that iteratively designs a personalized audio processing algorithm through situated interactions with a human client. The target application of AIDA is to propose on-the-spot the most interesting alternative values for the tuning parameters of a hearing aid (HA) algorithm, whenever a HA client is not satisfied with their HA performance. AIDA interprets searching for the "most interesting alternative" as an issue of optimal (acoustic) context-aware Bayesian trial design. In computational terms, AIDA is realized as an active inference-based agent with an Expected Free Energy criterion for trial design. This type of architecture is inspired by neuro-economic models on efficient (Bayesian) trial design in brains and implies that AIDA comprises generative probabilistic models for acoustic signals and user responses. We propose a novel generative model for acoustic signals as a sum of time-varying auto-regressive filters and a user response model based on a Gaussian Process Classifier. The full AIDA agent has been implemented in a factor graph for the generative model and all tasks (parameter learning, acoustic context classification, trial design, etc.) are realized by variational message passing on the factor graph. All verification and validation experiments and demonstrations are freely accessible at our GitHub repository.
Prevalence Threshold and bounds in the Accuracy of Binary Classification Systems
Authors: Jacques Balayla
Date: 2021-12-25 00:00:00
Tasks: Binary Classification, Classification

The accuracy of binary classification systems is defined as the proportion of correct predictions - both positive and negative - made by a classification model or computational algorithm. A value between 0 (no accuracy) and 1 (perfect accuracy), the accuracy of a classification model is dependent on several factors, notably: the classification rule or algorithm used, the intrinsic characteristics of the tool used to do the classification, and the relative frequency of the elements being classified. Several accuracy metrics exist, each with its own advantages in different classification scenarios. In this manuscript, we show that relative to a perfect accuracy of 1, the positive prevalence threshold ($\phi_e$), a critical point of maximum curvature in the precision-prevalence curve, bounds the $F{_{\beta}}$ score between 1 and 1.8/1.5/1.2 for $\beta$ values of 0.5/1.0/2.0, respectively; the $F_1$ score between 1 and 1.5, and the Fowlkes-Mallows Index (FM) between 1 and $\sqrt{2} \approx 1.414$. We likewise describe a novel $negative$ prevalence threshold ($\phi_n$), the level of sharpest curvature for the negative predictive value-prevalence curve, such that $\phi_n$ $>$ $\phi_e$. The area between both these thresholds bounds the Matthews Correlation Coefficient (MCC) between $\sqrt{2}/2$ and $\sqrt{2}$. Conversely, the ratio of the maximum possible accuracy to that at any point below the prevalence threshold, $\phi_e$, goes to infinity with decreasing prevalence. Though applications are numerous, the ideas herein discussed may be used in computational complexity theory, artificial intelligence, and medical screening, amongst others. Where computational time is a limiting resource, attaining the prevalence threshold in binary classification systems may be sufficient to yield levels of accuracy comparable to that under maximum prevalence.
On Dynamic Pricing with Covariates
Authors: Hanzhao Wang, Kalyan Talluri, Xiaocheng Li
Date: 2021-12-25 00:00:00
Tasks: Thompson Sampling

We consider dynamic pricing with covariates under a generalized linear demand model: a seller can dynamically adjust the price of a product over a horizon of $T$ time periods, and at each time period $t$, the demand of the product is jointly determined by the price and an observable covariate vector $x_t\in\mathbb{R}^d$ through a generalized linear model with unknown co-efficients. Most of the existing literature assumes the covariate vectors $x_t$'s are independently and identically distributed (i.i.d.); the few papers that relax this assumption either sacrifice model generality or yield sub-optimal regret bounds. In this paper, we show that UCB and Thompson sampling-based pricing algorithms can achieve an $O(d\sqrt{T}\log T)$ regret upper bound without assuming any statistical structure on the covariates $x_t$. Our upper bound on the regret matches the lower bound up to logarithmic factors. We thus show that (i) the i.i.d. assumption is not necessary for obtaining low regret, and (ii) the regret bound can be independent of the (inverse) minimum eigenvalue of the covariance matrix of the $x_t$'s, a quantity present in previous bounds. Moreover, we consider a constrained setting of the dynamic pricing problem where there is a limited and unreplenishable inventory and we develop theoretical results that relate the best achievable algorithm performance to a variation measure with respect to the temporal distribution shift of the covariates. We also discuss conditions under which a better regret is achievable and demonstrate the proposed algorithms' performance with numerical experiments.
A Spectral Method for Joint Community Detection and Orthogonal Group Synchronization
Authors: Yifeng Fan, Yuehaw Khoo, Zhizhen Zhao
Date: 2021-12-25 00:00:00
Tasks: Community Detection

Community detection and orthogonal group synchronization are both fundamental problems with a variety of important applications in science and engineering. In this work, we consider the joint problem of community detection and orthogonal group synchronization which aims to recover the communities and perform synchronization simultaneously. To this end, we propose a simple algorithm that consists of a spectral decomposition step followed by a blockwise column pivoted QR factorization (CPQR). The proposed algorithm is efficient and scales linearly with the number of edges in the graph. We also leverage the recently developed `leave-one-out' technique to establish a near-optimal guarantee for exact recovery of the cluster memberships and stable recovery of the orthogonal transforms. Numerical experiments demonstrate the efficiency and efficacy of our algorithm and confirm our theoretical characterization of it.
Application of Markov Structure of Genomes to Outlier Identification and Read Classification
Authors: Alan F. Karr, Jason Hauzel, Adam A. Porter, Marcel Schaefer
Date: 2021-12-24 00:00:00

In this paper we apply the structure of genomes as second-order Markov processes specified by the distributions of successive triplets of bases to two bioinformatics problems: identification of outliers in genome databases and read classification in metagenomics, using real coronavirus and adenovirus data.
Stability analysis of heterogeneous oligopoly games of increasing players with quadratic costs
Authors: Xiaoliang Li
Date: 2021-12-24 00:00:00

In this discussion draft, we explore heterogeneous oligopoly games of increasing players with quadratic costs, where the market is supposed to have the isoelastic demand. For each of the models considered in this draft, we analytically investigate the necessary and sufficient condition of the local stability of its positive equilibrium. Furthermore, we rigorously prove that the stability regions are enlarged as the number of involved firms is increasing.
Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression
Authors: Konstantin T. Matchev, Katia Matcheva, Alexander Roman
Date: 2021-12-22 00:00:00
Tasks: Physical Intuition, regression, Symbolic Regression

The physical characteristics and atmospheric chemical composition of newly discovered exoplanets are often inferred from their transit spectra which are obtained from complex numerical models of radiative transfer. Alternatively, simple analytical expressions provide insightful physical intuition into the relevant atmospheric processes. The deep learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. As a proof of concept, we successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot Jupiter exoplanets to derive a corresponding analytical formula. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables and reduce the number of independent inputs, which improves the performance of the symbolic regression. The dimensional analysis also allowed us to mathematically derive and properly parametrize the most general family of degeneracies among the input atmospheric parameters which affect the characterization of an exoplanet atmosphere through transit spectroscopy.
Measuring Quality of DNA Sequence Data via Degradation
Authors: Alan F. Karr, Jason Hauzel, Adam A. Porter, Marcel Schaefer
Date: 2021-12-24 00:00:00

We propose and apply a novel paradigm for characterization of genome data quality, which quantifies the effects of intentional degradation of quality. The rationale is that the higher the initial quality, the more fragile the genome and the greater the effects of degradation. We demonstrate that this phenomenon is ubiquitous, and that quantified measures of degradation can be used for multiple purposes. We focus on identifying outliers that may be problematic with respect to data quality, but might also be true anomalies or even attempts to subvert the database.
Accelerated and instance-optimal policy evaluation with linear function approximation
Authors: Tianjiao Li, Guanghui Lan, Ashwin Pananjady
Date: 2021-12-24 00:00:00

We study the problem of policy evaluation with linear function approximation and present efficient and practical algorithms that come with strong optimality guarantees. We begin by proving lower bounds that establish baselines on both the deterministic error and stochastic error in this problem. In particular, we prove an oracle complexity lower bound on the deterministic error in an instance-dependent norm associated with the stationary distribution of the transition kernel, and use the local asymptotic minimax machinery to prove an instance-dependent lower bound on the stochastic error in the i.i.d. observation model. Existing algorithms fail to match at least one of these lower bounds: To illustrate, we analyze a variance-reduced variant of temporal difference learning, showing in particular that it fails to achieve the oracle complexity lower bound. To remedy this issue, we develop an accelerated, variance-reduced fast temporal difference algorithm (VRFTD) that simultaneously matches both lower bounds and attains a strong notion of instance-optimality. Finally, we extend the VRFTD algorithm to the setting with Markovian observations, and provide instance-dependent convergence results. Our theoretical guarantees of optimality are corroborated by numerical experiments.
Gaussian Process Bandits with Aggregated Feedback
Authors: Mengyan Zhang, Russell Tsuchida, Cheng Soon Ong
Date: 2021-12-24 00:00:00

We consider the continuum-armed bandits problem, under a novel setting of recommending the best arms within a fixed budget under aggregated feedback. This is motivated by applications where the precise rewards are impossible or expensive to obtain, while an aggregated reward or feedback, such as the average over a subset, is available. We constrain the set of reward functions by assuming that they are from a Gaussian Process and propose the Gaussian Process Optimistic Optimisation (GPOO) algorithm. We adaptively construct a tree with nodes as subsets of the arm space, where the feedback is the aggregated reward of representatives of a node. We propose a new simple regret notion with respect to aggregated feedback on the recommended arms. We provide theoretical analysis for the proposed algorithm, and recover single point feedback as a special case. We illustrate GPOO and compare it with related algorithms on simulated data.
Toeplitz Least Squares Problems, Fast Algorithms and Big Data
Authors: Ali Eshragh, Oliver Di Pietro, Michael A. Saunders
Date: 2021-12-24 00:00:00
Tasks: Time Series, Time Series Analysis

In time series analysis, when fitting an autoregressive model, one must solve a Toeplitz ordinary least squares problem numerous times to find an appropriate model, which can severely affect computational times with large data sets. Two recent algorithms (LSAR and Repeated Halving) have applied randomized numerical linear algebra (RandNLA) techniques to fitting an autoregressive model to big time-series data. We investigate and compare the quality of these two approximation algorithms on large-scale synthetic and real-world data. While both algorithms display comparable results for synthetic datasets, the LSAR algorithm appears to be more robust when applied to real-world time series data. We conclude that RandNLA is effective in the context of big-data time series.
Is Importance Weighting Incompatible with Interpolating Classifiers?
Authors: Ke Alexander Wang, Niladri S. Chatterji, Saminul Haque, Tatsunori Hashimoto
Date: 2021-12-24 00:00:00
Proceeding: ICLR 2022 4

Importance weighting is a classic technique to handle distribution shifts. However, prior work has presented strong empirical and theoretical evidence demonstrating that importance weights can have little to no effect on overparameterized neural networks. Is importance weighting truly incompatible with the training of overparameterized neural networks? Our paper answers this in the negative. We show that importance weighting fails not because of the overparameterization, but instead, as a result of using exponentially-tailed losses like the logistic or cross-entropy loss. As a remedy, we show that polynomially-tailed losses restore the effects of importance reweighting in correcting distribution shift in overparameterized models. We characterize the behavior of gradient descent on importance weighted polynomially-tailed losses with overparameterized linear models, and theoretically demonstrate the advantage of using polynomially-tailed losses in a label shift setting. Surprisingly, our theory shows that using weights that are obtained by exponentiating the classical unbiased importance weights can improve performance. Finally, we demonstrate the practical value of our analysis with neural network experiments on a subpopulation shift and a label shift dataset. When reweighted, our loss function can outperform reweighted cross-entropy by as much as 9% in test accuracy. Our loss function also gives test accuracies comparable to, or even exceeding, well-tuned state-of-the-art methods for correcting distribution shifts.
Tractable and Near-Optimal Adversarial Algorithms for Robust Estimation in Contaminated Gaussian Models
Authors: Ziyue Wang, Zhiqiang Tan
Date: 2021-12-24 00:00:00

Consider the problem of simultaneous estimation of location and variance matrix under Huber's contaminated Gaussian model. First, we study minimum $f$-divergence estimation at the population level, corresponding to a generative adversarial method with a nonparametric discriminator and establish conditions on $f$-divergences which lead to robust estimation, similarly to robustness of minimum distance estimation. More importantly, we develop tractable adversarial algorithms with simple spline discriminators, which can be implemented via nested optimization such that the discriminator parameters can be fully updated by maximizing a concave objective function given the current generator. The proposed methods are shown to achieve minimax optimal rates or near-optimal rates depending on the $f$-divergence and the penalty used. This is the first time such near-optimal error rates are established for adversarial algorithms with linear discriminators under Huber's contamination model. We present simulation studies to demonstrate advantages of the proposed methods over classic robust estimators, pairwise methods, and a generative adversarial method with neural network discriminators.
Optimal Variable Clustering for High-Dimensional Matrix Valued Data
Authors: Inbeom Lee, Siyi Deng, Yang Ning
Date: 2021-12-24 00:00:00
Tasks: Clustering, Vocal Bursts Intensity Prediction

Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which can be very informative, especially in high-dimensional settings or when mean information is not available. To extract the information from the dependence structure for clustering, we propose a new latent variable model for the features arranged in matrix form, with some unknown membership matrices representing the clusters for the rows and columns. Under this model, we further propose a class of hierarchical clustering algorithms using the difference of a weighted covariance matrix as the dissimilarity measure. Theoretically, we show that under mild conditions, our algorithm attains clustering consistency in the high-dimensional setting. While this consistency result holds for our algorithm with a broad class of weighted covariance matrices, the conditions for this result depend on the choice of the weight. To investigate how the weight affects the theoretical performance of our algorithm, we establish the minimax lower bound for clustering under our latent variable model in terms of some cluster separation metric. Given these results, we identify the optimal weight in the sense that using this weight guarantees our algorithm to be minimax rate-optimal. The practical implementation of our algorithm with the optimal weight is also discussed. Simulation studies show that our algorithm performs better than existing methods in terms of the adjusted Rand index (ARI). The method is applied to a genomic dataset and yields meaningful interpretations.
When Random Tensors meet Random Matrices
Authors: Mohamed El Amine Seddik, Maxime Guillaud, Romain Couillet
Date: 2021-12-23 00:00:00
Tasks: LEMMA

Relying on random matrix theory (RMT), this paper studies asymmetric order-$d$ spiked tensor models with Gaussian noise. Using the variational definition of the singular vectors and values of (Lim, 2005), we show that the analysis of the considered model boils down to the analysis of an equivalent spiked symmetric \textit{block-wise} random matrix, that is constructed from \textit{contractions} of the studied tensor with the singular vectors associated to its best rank-1 approximation. Our approach allows the exact characterization of the almost sure asymptotic singular value and alignments of the corresponding singular vectors with the true spike components, when $\frac{n_i}{\sum_{j=1}^d n_j}\to c_i\in (0, 1)$ with $n_i$'s the tensor dimensions. In contrast to other works that rely mostly on tools from statistical physics to study random tensors, our results rely solely on classical RMT tools such as Stein's lemma. Finally, classical RMT results concerning spiked random matrices are recovered as a particular case.
Surrogate Likelihoods for Variational Annealed Importance Sampling
Authors: Martin Jankowiak, Du Phan
Date: 2021-12-22 00:00:00
Tasks: Bayesian Inference, Probabilistic Programming, Variational Inference

Variational inference is a powerful paradigm for approximate Bayesian inference with a number of appealing properties, including support for model learning and data subsampling. By contrast MCMC methods like Hamiltonian Monte Carlo do not share these properties but remain attractive since, contrary to parametric methods, MCMC is asymptotically unbiased. For these reasons researchers have sought to combine the strengths of both classes of algorithms, with recent approaches coming closer to realizing this vision in practice. However, supporting data subsampling in these hybrid methods can be a challenge, a shortcoming that we address by introducing a surrogate likelihood that can be learned jointly with other variational parameters. We argue theoretically that the resulting algorithm permits the user to make an intuitive trade-off between inference fidelity and computational cost. In an extensive empirical comparison we show that our method performs well in practice and that it is well-suited for black-box inference in probabilistic programming frameworks.