pwc-archive/papers-with-abstracts huggingface dataset:
Correlated Product of Experts for Sparse Gaussian Process Regression
Authors: Manuel Schürch, Dario Azzimonti, Alessio Benavoli, Marco Zaffalon
Date: 2021-12-17 00:00:00
Tasks: Gaussian Processes, regression, Stochastic Optimization

Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with well-calibrated uncertainty estimates, however, off-the-shelf GP inference procedures are limited to datasets with several thousand data points because of their cubic computational complexity. For this reason, many sparse GPs techniques have been developed over the past years. In this paper, we focus on GP regression tasks and propose a new approach based on aggregating predictions from several local and correlated experts. Thereby, the degree of correlation between the experts can vary between independent up to fully correlated experts. The individual predictions of the experts are aggregated taking into account their correlation resulting in consistent uncertainty estimates. Our method recovers independent Product of Experts, sparse GP and full GP in the limiting cases. The presented framework can deal with a general kernel function and multiple variables, and has a time and space complexity which is linear in the number of experts and data samples, which makes our approach highly scalable. We demonstrate superior performance, in a time vs. accuracy sense, of our proposed method against state-of-the-art GP approximation methods for synthetic as well as several real-world datasets with deterministic and stochastic optimization.
Fair Active Learning: Solving the Labeling Problem in Insurance
Authors: Romuald Elie, Caroline Hillairet, François Hu, Marc Juillard
Date: 2021-12-17 00:00:00
Tasks: Active Learning, Fairness

This paper addresses significant obstacles that arise from the widespread use of machine learning models in the insurance industry, with a specific focus on promoting fairness. The initial challenge lies in effectively leveraging unlabeled data in insurance while reducing the labeling effort and emphasizing data relevance through active learning techniques. The paper explores various active learning sampling methodologies and evaluates their impact on both synthetic and real insurance datasets. This analysis highlights the difficulty of achieving fair model inferences, as machine learning models may replicate biases and discrimination found in the underlying data. To tackle these interconnected challenges, the paper introduces an innovative fair active learning method. The proposed approach samples informative and fair instances, achieving a good balance between model predictive performance and fairness, as confirmed by numerical experiments on insurance datasets.
A random energy approach to deep learning
Authors: Rongrong Xie, Matteo Marsili
Date: 2021-12-17 00:00:00
Tasks: Deep Learning

We study a generic ensemble of deep belief networks which is parametrized by the distribution of energy levels of the hidden states of each layer. We show that, within a random energy approach, statistical dependence can propagate from the visible to deep layers only if each layer is tuned close to the critical point during learning. As a consequence, efficiently trained learning machines are characterised by a broad distribution of energy levels. The analysis of Deep Belief Networks and Restricted Boltzmann Machines on different datasets confirms these conclusions.
Improving evidential deep learning via multi-task learning
Authors: Dongpin Oh, Bonggun Shin
Date: 2021-12-17 00:00:00
Tasks: Deep Learning, Multi-Task Learning, Out-of-Distribution Detection, regression

The Evidential regression network (ENet) estimates a continuous target and its predictive uncertainty without costly Bayesian model averaging. However, it is possible that the target is inaccurately predicted due to the gradient shrinkage problem of the original loss function of the ENet, the negative log marginal likelihood (NLL) loss. In this paper, the objective is to improve the prediction accuracy of the ENet while maintaining its efficient uncertainty estimation by resolving the gradient shrinkage problem. A multi-task learning (MTL) framework, referred to as MT-ENet, is proposed to accomplish this aim. In the MTL, we define the Lipschitz modified mean squared error (MSE) loss function as another loss and add it to the existing NLL loss. The Lipschitz modified MSE loss is designed to mitigate the gradient conflict with the NLL loss by dynamically adjusting its Lipschitz constant. By doing so, the Lipschitz MSE loss does not disturb the uncertainty estimation of the NLL loss. The MT-ENet enhances the predictive accuracy of the ENet without losing uncertainty estimation capability on the synthetic dataset and real-world benchmarks, including drug-target affinity (DTA) regression. Furthermore, the MT-ENet shows remarkable calibration and out-of-distribution detection capability on the DTA benchmarks.
Unadjusted Langevin algorithm for sampling a mixture of weakly smooth potentials
Authors: Dao Nguyen
Date: 2021-12-17 00:00:00

Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, it seems to be a considerable restriction when the potentials are often required to be smooth (gradient Lipschitz). This paper studies the problem of sampling through Euler discretization, where the potential function is assumed to be a mixture of weakly smooth distributions and satisfies weakly dissipative. We establish the convergence in Kullback-Leibler (KL) divergence with the number of iterations to reach $\epsilon$-neighborhood of a target distribution in only polynomial dependence on the dimension. We relax the degenerated convex at infinity conditions of \citet{erdogdu2020convergence} and prove convergence guarantees under Poincar\'{e} inequality or non-strongly convex outside the ball. In addition, we also provide convergence in $L_{\beta}$-Wasserstein metric for the smoothing potential.
Gaussian RBF Centered Kernel Alignment (CKA) in the Large Bandwidth Limit
Authors: Sergio A. Alvarez
Date: 2021-12-17 00:00:00

We prove that Centered Kernel Alignment (CKA) based on a Gaussian RBF kernel converges to linear CKA in the large-bandwidth limit. We show that convergence onset is sensitive to the geometry of the feature representations, and that representation eccentricity bounds the range of bandwidths for which Gaussian CKA behaves nonlinearly.
Robust Upper Bounds for Adversarial Training
Authors: Dimitris Bertsimas, Xavier Boix, Kimberly Villalobos Carballo, Dick den Hertog
Date: 2021-12-17 00:00:00

Many state-of-the-art adversarial training methods for deep learning leverage upper bounds of the adversarial loss to provide security guarantees against adversarial attacks. Yet, these methods rely on convex relaxations to propagate lower and upper bounds for intermediate layers, which affect the tightness of the bound at the output layer. We introduce a new approach to adversarial training by minimizing an upper bound of the adversarial loss that is based on a holistic expansion of the network instead of separate bounds for each layer. This bound is facilitated by state-of-the-art tools from Robust Optimization; it has closed-form and can be effectively trained using backpropagation. We derive two new methods with the proposed approach. The first method (Approximated Robust Upper Bound or aRUB) uses the first order approximation of the network as well as basic tools from Linear Robust Optimization to obtain an empirical upper bound of the adversarial loss that can be easily implemented. The second method (Robust Upper Bound or RUB), computes a provable upper bound of the adversarial loss. Across a variety of tabular and vision data sets we demonstrate the effectiveness of our approach -- RUB is substantially more robust than state-of-the-art methods for larger perturbations, while aRUB matches the performance of state-of-the-art methods for small perturbations.
High-Dimensional Inference in Bayesian Networks
Authors: Fritz M. Bayer, Giusi Moffa, Niko Beerenwinkel, Jack Kuipers
Date: 2021-12-16 00:00:00
Tasks: Benchmarking, Vocal Bursts Intensity Prediction

Inference of the marginal probability distribution is defined as the calculation of the probability of a subset of the variables and is relevant for handling missing data and hidden variables. While inference of the marginal probability distribution is crucial for various problems in machine learning and statistics, its exact computation is generally not feasible for categorical variables in Bayesian networks due to the NP-hardness of this task. We develop a divide-and-conquer approach using the graphical properties of Bayesian networks to split the computation of the marginal probability distribution into sub-calculations of lower dimensionality, thus reducing the overall computational complexity. Exploiting this property, we present an efficient and scalable algorithm for calculating the marginal probability distribution for categorical variables. The novel method is compared against state-of-the-art approximate inference methods in a benchmarking study, where it displays superior performance. As an immediate application, we demonstrate how our method can be used to classify incomplete data against Bayesian networks and use this approach for identifying the cancer subtype of kidney cancer patient samples.
Analysis of Generalized Bregman Surrogate Algorithms for Nonsmooth Nonconvex Statistical Learning
Authors: Yiyuan She, Zhifeng Wang, Jiuwu Jin
Date: 2021-12-16 00:00:00
Tasks: Sparse Learning

Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror descent, iterative thresholding, DC programming and many others as particular instances. The recharacterization via generalized Bregman functions enables us to construct suitable error measures and establish global convergence rates for nonconvex and nonsmooth objectives in possibly high dimensions. For sparse learning problems with a composite objective, under some regularity conditions, the obtained estimators as the surrogate's fixed points, though not necessarily local minimizers, enjoy provable statistical guarantees, and the sequence of iterates can be shown to approach the statistical truth within the desired accuracy geometrically fast. The paper also studies how to design adaptive momentum based accelerations without assuming convexity or smoothness by carefully controlling stepsize and relaxation parameters.
A Statistics and Deep Learning Hybrid Method for Multivariate Time Series Forecasting and Mortality Modeling
Authors: Thabang Mathonsi, Terence L. Van Zyl
Date: 2021-12-16 00:00:00
Tasks: Multivariate Time Series Forecasting, Prediction Intervals, Time Series, Time Series Analysis, Time Series Forecasting

Hybrid methods have been shown to outperform pure statistical and pure deep learning methods at forecasting tasks and quantifying the associated uncertainty with those forecasts (prediction intervals). One example is Exponential Smoothing Recurrent Neural Network (ES-RNN), a hybrid between a statistical forecasting model and a recurrent neural network variant. ES-RNN achieves a 9.4\% improvement in absolute error in the Makridakis-4 Forecasting Competition. This improvement and similar outperformance from other hybrid models have primarily been demonstrated only on univariate datasets. Difficulties with applying hybrid forecast methods to multivariate data include ($i$) the high computational cost involved in hyperparameter tuning for models that are not parsimonious, ($ii$) challenges associated with auto-correlation inherent in the data, as well as ($iii$) complex dependency (cross-correlation) between the covariates that may be hard to capture. This paper presents Multivariate Exponential Smoothing Long Short Term Memory (MES-LSTM), a generalized multivariate extension to ES-RNN, that overcomes these challenges. MES-LSTM utilizes a vectorized implementation. We test MES-LSTM on several aggregated coronavirus disease of 2019 (COVID-19) morbidity datasets and find our hybrid approach shows consistent, significant improvement over pure statistical and deep learning methods at forecast accuracy and prediction interval construction.
Trading with the Momentum Transformer: An Intelligent and Interpretable Architecture
Authors: Kieran Wood, Sven Giegerich, Stephen Roberts, Stefan Zohren
Date: 2021-12-16 00:00:00
Tasks: Time Series, Time Series Analysis, Variable Selection

We introduce the Momentum Transformer, an attention-based deep-learning architecture, which outperforms benchmark time-series momentum and mean-reversion trading strategies. Unlike state-of-the-art Long Short-Term Memory (LSTM) architectures, which are sequential in nature and tailored to local processing, an attention mechanism provides our architecture with a direct connection to all previous time-steps. Our architecture, an attention-LSTM hybrid, enables us to learn longer-term dependencies, improves performance when considering returns net of transaction costs and naturally adapts to new market regimes, such as during the SARS-CoV-2 crisis. Via the introduction of multiple attention heads, we can capture concurrent regimes, or temporal dynamics, which are occurring at different timescales. The Momentum Transformer is inherently interpretable, providing us with greater insights into our deep-learning momentum trading strategy, including the importance of different factors over time and the past time-steps which are of the greatest significance to the model.
Gaining Outlier Resistance with Progressive Quantiles: Fast Algorithms and Theoretical Studies
Authors: Yiyuan She, Zhifeng Wang, Jiahui Shen
Date: 2021-12-15 00:00:00

Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a close connection to the method of trimming and includes explicit outlyingness parameters for all samples, which in turn facilitates computation, theory, and parameter tuning. To tackle the issues of nonconvexity and nonsmoothness, we develop scalable algorithms with implementation ease and guaranteed fast convergence. In particular, a new technique is proposed to alleviate the requirement on the starting point such that on regular datasets, the number of data resamplings can be substantially reduced. Based on combined statistical and computational treatments, we are able to perform nonasymptotic analysis beyond M-estimation. The obtained resistant estimators, though not necessarily globally or even locally optimal, enjoy minimax rate optimality in both low dimensions and high dimensions. Experiments in regression, classification, and neural networks show excellent performance of the proposed methodology at the occurrence of gross outliers.
Real-time Detection of Anomalies in Multivariate Time Series of Astronomical Data
Authors: Daniel Muthukrishna, Kaisey S. Mandel, Michelle Lochner, Sara Webb, Gautham Narayan
Date: 2021-12-15 00:00:00
Tasks: Anomaly Detection, Astronomy, Attribute, Time Series, Time Series Analysis

Astronomical transients are stellar objects that become temporarily brighter on various timescales and have led to some of the most significant discoveries in cosmology and astronomy. Some of these transients are the explosive deaths of stars known as supernovae while others are rare, exotic, or entirely new kinds of exciting stellar explosions. New astronomical sky surveys are observing unprecedented numbers of multi-wavelength transients, making standard approaches of visually identifying new and interesting transients infeasible. To meet this demand, we present two novel methods that aim to quickly and automatically detect anomalous transient light curves in real-time. Both methods are based on the simple idea that if the light curves from a known population of transients can be accurately modelled, any deviations from model predictions are likely anomalies. The first approach is a probabilistic neural network built using Temporal Convolutional Networks (TCNs) and the second is an interpretable Bayesian parametric model of a transient. We show that the flexibility of neural networks, the attribute that makes them such a powerful tool for many regression tasks, is what makes them less suitable for anomaly detection when compared with our parametric model.
Leveraging Image-based Generative Adversarial Networks for Time Series Generation
Authors: Justin Hellermann, Stefan Lessmann
Date: 2021-12-15 00:00:00
Tasks: Disentanglement, Time Series, Time Series Analysis, Time Series Generation

Generative models for images have gained significant attention in computer vision and natural language processing due to their ability to generate realistic samples from complex data distributions. To leverage the advances of image-based generative models for the time series domain, we propose a two-dimensional image representation for time series, the Extended Intertemporal Return Plot (XIRP). Our approach captures the intertemporal time series dynamics in a scale-invariant and invertible way, reducing training time and improving sample quality. We benchmark synthetic XIRPs obtained by an off-the-shelf Wasserstein GAN with gradient penalty (WGAN-GP) to other image representations and models regarding similarity and predictive ability metrics. Our novel, validated image representation for time series consistently and significantly outperforms a state-of-the-art RNN-based generative model regarding predictive ability. Further, we introduce an improved stochastic inversion to substantially improve simulation quality regardless of the representation and provide the prospect of transfer potentials in other domains.
Supervised learning of analysis-sparsity priors with automatic differentiation
Authors: Hashem Ghanem, Joseph Salmon, Nicolas Keriven, Samuel Vaiter
Date: 2021-12-15 00:00:00
Tasks: Denoising, Image Reconstruction

Sparsity priors are commonly used in denoising and image reconstruction. For analysis-type priors, a dictionary defines a representation of signals that is likely to be sparse. In most situations, this dictionary is not known, and is to be recovered from pairs of ground-truth signals and measurements, by minimizing the reconstruction error. This defines a hierarchical optimization problem, which can be cast as a bi-level optimization. Yet, this problem is unsolvable, as reconstructions and their derivative wrt the dictionary have no closed-form expression. However, reconstructions can be iteratively computed using the Forward-Backward splitting (FB) algorithm. In this paper, we approximate reconstructions by the output of the aforementioned FB algorithm. Then, we leverage automatic differentiation to evaluate the gradient of this output wrt the dictionary, which we learn with projected gradient descent. Experiments show that our algorithm successfully learns the 1D Total Variation (TV) dictionary from piecewise constant signals. For the same case study, we propose to constrain our search to dictionaries of 0-centered columns, which removes undesired local minima and improves numerical stability.
Understanding Public Opinion on Using Hydroxychloroquine for COVID-19 Treatment via Social Media
Authors: Thuy T. Do, Du Nguyen, Anh Le, Anh Nguyen, Dong Nguyen, Nga Hoang, Uyen Le, Tuan Tran
Date: 2022-01-01 00:00:00
Tasks: Descriptive, Sentiment Analysis

Hydroxychloroquine (HCQ) is used to prevent or treat malaria caused by mosquito bites. Recently, the drug has been suggested to treat COVID-19, but that has not been supported by scientific evidence. The information regarding the drug efficacy has flooded social networks, posting potential threats to the community by perverting their perceptions of the drug efficacy. This paper studies the reactions of social network users on the recommendation of using HCQ for COVID-19 treatment by analyzing the reaction patterns and sentiment of the tweets. We collected 164,016 tweets from February to December 2020 and used a text mining approach to identify social reaction patterns and opinion change over time. Our descriptive analysis identified an irregularity of the users' reaction patterns associated tightly with the social and news feeds on the development of HCQ and COVID-19 treatment. The study linked the tweets and Google search frequencies to reveal the viewpoints of local communities on the use of HCQ for COVID-19 treatment across different states. Further, our tweet sentiment analysis reveals that public opinion changed significantly over time regarding the recommendation of using HCQ for COVID-19 treatment. The data showed that high support in the early dates but it significantly declined in October. Finally, using the manual classification of 4,850 tweets by humans as our benchmark, our sentiment analysis showed that the Google Cloud Natural Language algorithm outperformed the Valence Aware Dictionary and sEntiment Reasoner in classifying tweets, especially in the sarcastic tweet group.
Bayesian Graph Contrastive Learning
Authors: Arman Hasanzadeh, Mohammadreza Armandpour, Ehsan Hajiramezanali, Mingyuan Zhou, Nick Duffield, Krishna Narayanan
Date: 2021-12-15 00:00:00
Tasks: Contrastive Learning, Self-Supervised Learning, Uncertainty Quantification

Contrastive learning has become a key component of self-supervised learning approaches for graph-structured data. Despite their success, existing graph contrastive learning methods are incapable of uncertainty quantification for node representations or their downstream tasks, limiting their application in high-stakes domains. In this paper, we propose a novel Bayesian perspective of graph contrastive learning methods showing random augmentations leads to stochastic encoders. As a result, our proposed method represents each node by a distribution in the latent space in contrast to existing techniques which embed each node to a deterministic vector. By learning distributional representations, we provide uncertainty estimates in downstream graph analytics tasks and increase the expressive power of the predictive model. In addition, we propose a Bayesian framework to infer the probability of perturbations in each view of the contrastive model, eliminating the need for a computationally expensive search for hyperparameter tuning. We empirically show a considerable improvement in performance compared to existing state-of-the-art methods on several benchmark datasets.
Variable Selection and Regularization via Arbitrary Rectangle-range Generalized Elastic Net
Authors: Yujia Ding, Qidi Peng, Zhengming Song, Hansen Chen
Date: 2021-12-14 00:00:00
Tasks: Variable Selection

We introduce the arbitrary rectangle-range generalized elastic net penalty method, abbreviated to ARGEN, for performing constrained variable selection and regularization in high-dimensional sparse linear models. As a natural extension of the nonnegative elastic net penalty method, ARGEN is proved to have variable selection consistency and estimation consistency under some conditions. The asymptotic behavior in distribution of the ARGEN estimators have been studied. We also propose an algorithm called MU-QP-RR-W-$l_1$ to efficiently solve ARGEN. By conducting simulation study we show that ARGEN outperforms the elastic net in a number of settings. Finally an application of S&P 500 index tracking with constraints on the stock allocations is performed to provide general guidance for adapting ARGEN to solve real-world problems.