arXiv subjects

Shrijita Bhattacharya

Publications and source records attributed to Shrijita Bhattacharya.

13 recordsLinked to original sources

arXiv2024

Spike-and-slab shrinkage priors for structurally sparse Bayesian neural networks

Network complexity and computational efficiency have become increasingly significant aspects of deep learning. Sparse deep learning addresses these challenges by recovering a sparse representation of the underlying target function by reducing heavily over-parameterized deep neural networks. Specifically, deep neural architectures compressed via structured sparsity (e.g. node sparsity) provide low latency inference, higher data throughput, and reduced energy consumption. In this paper, we explore two well-established shrinkage techniques, Lasso and Horseshoe, for model compression in Bayesian neural networks. To this end, we propose structurally sparse Bayesian neural networks which systematically prune excessive nodes with (i) Spike-and-Slab Group Lasso (SS-GL), and (ii) Spike-and-Slab Group Horseshoe (SS-GHS) priors, and develop computationally tractable variational inference including continuous relaxation of Bernoulli variables. We establish the contraction rates of the variational posterior of our proposed models as a function of the network topology, layer-wise node cardinalities, and bounds on the network weights. We empirically demonstrate the competitive performance of our models compared to the baseline models in prediction accuracy, model compression, and inference latency.

stat.ML↗

arXiv2024

Sequential Bayesian Neural Subnetwork Ensembles

Deep ensembles have emerged as a powerful technique for improving predictive performance and enhancing model robustness across various applications by leveraging model diversity. However, traditional deep ensemble methods are often computationally expensive and rely on deterministic models, which may limit their flexibility. Additionally, while sparse subnetworks of dense models have shown promise in matching the performance of their dense counterparts and even enhancing robustness, existing methods for inducing sparsity typically incur training costs comparable to those of training a single dense model, as they either gradually prune the network during training or apply thresholding post-training. In light of these challenges, we propose an approach for sequential ensembling of dynamic Bayesian neural subnetworks that consistently maintains reduced model complexity throughout the training process while generating diverse ensembles in a single forward pass. Our approach involves an initial exploration phase to identify high-performing regions within the parameter space, followed by multiple exploitation phases that take advantage of the compactness of the sparse model. These exploitation phases quickly converge to different minima in the energy landscape, corresponding to high-performing subnetworks that together form a diverse and robust ensemble. We empirically demonstrate that our proposed approach outperforms traditional dense and sparse deterministic and Bayesian ensemble models in terms of prediction accuracy, uncertainty estimation, out-of-distribution detection, and adversarial robustness.

stat.ML↗

arXiv2022

Layer Adaptive Node Selection in Bayesian Neural Networks: Statistical Guarantees and Implementation Details

Sparse deep neural networks have proven to be efficient for predictive model building in large-scale studies. Although several works have studied theoretical and numerical properties of sparse neural architectures, they have primarily focused on the edge selection. Sparsity through edge selection might be intuitively appealing; however, it does not necessarily reduce the structural complexity of a network. Instead pruning excessive nodes leads to a structurally sparse network with significant computational speedup during inference. To this end, we propose a Bayesian sparse solution using spike-and-slab Gaussian priors to allow for automatic node selection during training. The use of spike-and-slab prior alleviates the need of an ad-hoc thresholding rule for pruning. In addition, we adopt a variational Bayes approach to circumvent the computational challenges of traditional Markov Chain Monte Carlo (MCMC) implementation. In the context of node selection, we establish the fundamental result of variational posterior consistency together with the characterization of prior parameters. In contrast to the previous works, our theoretical development relaxes the assumptions of the equal number of nodes and uniform bounds on all network weights, thereby accommodating sparse networks with layer-dependent node structures or coefficient bounds. With a layer-wise characterization of prior inclusion probabilities, we discuss the optimal contraction rates of the variational posterior. We empirically demonstrate that our proposed approach outperforms the edge selection method in computational complexity with similar or better predictive performance. Our experimental evidence further substantiates that our theoretical work facilitates layer-wise optimal node recovery.

stat.ML↗

arXiv2022

Black Box Variational Bayesian Model Averaging

For many decades now, Bayesian Model Averaging (BMA) has been a popular framework to systematically account for model uncertainty that arises in situations when multiple competing models are available to describe the same or similar physical process. The implementation of this framework, however, comes with a multitude of practical challenges including posterior approximation via Markov Chain Monte Carlo and numerical integration. We present a Variational Bayesian Inference approach to BMA as a viable alternative to the standard solutions which avoids many of the aforementioned pitfalls. The proposed method is "black box" in the sense that it can be readily applied to many models with little to no model-specific derivation. We illustrate the utility of our variational approach on a suite of examples and discuss all the necessary implementation details. Fully documented Python code with all the examples is provided as well.

stat.CO↗

arXiv2021

Variational Bayes algorithm and posterior consistency of Ising model parameter estimation

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant in the likelihood. Here, we use a pseudo-likelihood instead to study the Bayesian estimation of two-parameter, inverse temperature, and magnetization, Ising model with a fully specified coupling matrix. We develop a computationally efficient variational Bayes procedure for model estimation. Under the Gaussian mean-field variational family, we derive posterior contraction rates of the variational posterior obtained under the pseudo-likelihood. We also discuss the loss incurred due to variational posterior over true posterior for the pseudo-likelihood approach. Extensive simulation studies validate the efficacy of mean-field Gaussian and bivariate Gaussian families as the possible choices of the variational family for inference of Ising model parameters.

stat.ME↗

arXiv2021

A Fast and Calibrated Computer Model Emulator: An Empirical Bayes Approach

Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and economical to run than physical experiments. In this work, we develop an empirical Bayes approach to predictions of physical quantities using a computer model, where we assume that the computer model under consideration needs to be calibrated and is computationally expensive. We propose a Gaussian process emulator and a Gaussian process model for the systematic discrepancy between the computer model and the underlying physical process. This allows for closed-form and easy-to-compute predictions given by a conditional distribution induced by the Gaussian processes. We provide a rigorous theoretical justification of the proposed approach by establishing posterior consistency of the estimated physical process. The computational efficiency of the methods is demonstrated in an extensive simulation study and a real data example. The newly established approach makes enhanced use of computer models both from practical and theoretical standpoints.

stat.CO↗

arXiv2020

Variational Bayes Neural Network: Posterior Consistency, Classification Accuracy and Computational Challenges

Bayesian neural network models (BNN) have re-surged in recent years due to the advancement of scalable computations and its utility in solving complex prediction problems in a wide variety of applications. Despite the popularity and usefulness of BNN, the conventional Markov Chain Monte Carlo based implementation suffers from high computational cost, limiting the use of this powerful technique in large scale studies. The variational Bayes inference has become a viable alternative to circumvent some of the computational issues. Although the approach is popular in machine learning, its application in statistics is somewhat limited. This paper develops a variational Bayesian neural network estimation methodology and related statistical theory. The numerical algorithms and their implementational are discussed in detail. The theory for posterior consistency, a desirable property in nonparametric Bayesian statistics, is also developed. This theory provides an assessment of prediction accuracy and guidelines for characterizing the prior distributions and variational family. The loss of using a variational posterior over the true posterior has also been quantified. The development is motivated by an important biomedical engineering application, namely building predictive tools for the transition from mild cognitive impairment to Alzheimer's disease. The predictors are multi-modal and may involve complex interactive relations.

stat.ML↗

arXiv2020

Quantile Regression Neural Networks: A Bayesian Approach

This article introduces a Bayesian neural network estimation method for quantile regression assuming an asymmetric Laplace distribution (ALD) for the response variable. It is shown that the posterior distribution for feedforward neural network quantile regression is asymptotically consistent under a misspecified ALD model. This consistency proof embeds the problem from density estimation domain and uses bounds on the bracketing entropy to derive the posterior consistency over Hellinger neighborhoods. This consistency result is shown in the setting where the number of hidden nodes grow with the sample size. The Bayesian implementation utilizes the normal-exponential mixture representation of the ALD density. The algorithm uses Markov chain Monte Carlo (MCMC) simulation technique - Gibbs sampling coupled with Metropolis-Hastings algorithm. We have addressed the issue of complexity associated with the afore-mentioned MCMC implementation in the context of chain convergence, choice of starting values, and step sizes. We have illustrated the proposed method with simulation studies and real data examples.

math.ST↗

arXiv2020

Statistical Foundation of Variational Bayes Neural Networks

Despite the popularism of Bayesian neural networks in recent years, its use is somewhat limited in complex and big data situations due to the computational cost associated with full posterior evaluations. Variational Bayes (VB) provides a useful alternative to circumvent the computational cost and time complexity associated with the generation of samples from the true posterior using Markov Chain Monte Carlo (MCMC) techniques. The efficacy of the VB methods is well established in machine learning literature. However, its potential broader impact is hindered due to a lack of theoretical validity from a statistical perspective. However there are few results which revolve around the theoretical properties of VB, especially in non-parametric problems. In this paper, we establish the fundamental result of posterior consistency for the mean-field variational posterior (VP) for a feed-forward artificial neural network model. The paper underlines the conditions needed to guarantee that the VP concentrates around Hellinger neighborhoods of the true density function. Additionally, the role of the scale parameter and its influence on the convergence rates has also been discussed. The paper mainly relies on two results (1) the rate at which the true posterior grows (2) the rate at which the KL-distance between the posterior and variational posterior grows. The theory provides a guideline of building prior distributions for Bayesian NN models along with an assessment of accuracy of the corresponding VB implementation.

stat.ML↗

arXiv2019

Outlier detection and a tail-adjusted boxplot based on extreme value theory

Whether an extreme observation is an outlier or not, depends strongly on the corresponding tail behaviour of the underlying distribution. We develop an automatic, data-driven method to identify extreme tail behaviour that deviates from the intermediate and central characteristics. This allows for detecting extreme outliers or sets of extreme data that show less spread than the bulk of the data. To this end we extend a testing method proposed in Bhattacharya et al 2019 for the specific case of heavy tailed models, to all max-domains of attraction. Consequently we propose a tail-adjusted boxplot which yields a more accurate representation of possible outliers. Several examples and simulation results illustrate the finite sample behaviour of this approach.

stat.ME↗

arXiv2018

Data-adaptive trimming of the Hill estimator and detection of outliers in the extremes of heavy-tailed data

We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample efficient among all unbiased estimators with a given strict upper break-down point. For general heavy-tailed models, we establish the asymptotic normality of the estimator under second order regular variation conditions and also show it is minimax rate-optimal in the Hall class of distributions. We also develop an automatic, data-driven method for the choice of the trimming parameter which yields a new type of robust estimator that can adapt to the unknown level of contamination in the extremes. This adaptive robustness property makes our estimator particularly appealing and superior to other robust estimators in the setting where the extremes of the data are contaminated. As an important application of the data-driven selection of the trimming parameters, we obtain a methodology for the principled identification of extreme outliers in heavy tailed data. Indeed, the method has been shown to correctly identify the number of outliers in the previously explored Condroz data set.

stat.ME↗

arXiv2017

Trimming the Hill estimator: robustness, optimality and adaptivity

We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample efficient among all unbiased estimators with a given strict upper break-down point. For general heavy-tailed models, we establish the asymptotic normality of the estimator under second order conditions and discuss its minimax optimal rate in the Hall class. We introduce the so-called trimmed Hill plot, which can be used to select the number of top order statistics to trim. We also develop an automatic, data-driven procedure for the choice of trimming. This results in a new type of robust estimator that can {\em adapt} to the unknown level of contamination in the extremes. As a by-product we also obtain a methodology for identifying extreme outliers in heavy tailed data. The competitive performance of the trimmed Hill and adaptive trimmed Hill estimators is illustrated with simulations.

stat.ME↗

arXiv2016

AMON: An Open Source Architecture for Online Monitoring, Statistical Analysis and Forensics of Multi-gigabit Streams

The Internet, as a global system of interconnected networks, carries an extensive array of information resources and services. Key requirements include good quality-of-service and protection of the infrastructure from nefarious activity (e.g. distributed denial of service--DDoS--attacks). Network monitoring is essential to network engineering, capacity planning and prevention / mitigation of threats. We develop an open source architecture, AMON (All-packet MONitor), for online monitoring and analysis of multi-gigabit network streams. It leverages the high-performance packet monitor PF RING and is readily deployable on commodity hardware. AMON examines all packets, partitions traffic into sub-streams by using rapid hashing and computes certain real-time data products. The resulting data structures provide views of the intensity and connectivity structure of network traffic at the time-scale of routing. The proposed integrated framework includes modules for the identification of heavy-hitters as well as for visualization and statistical detection at the time-of-onset of high impact events such as DDoS. This allows operators to quickly visualize and diagnose attacks, and limit offline and time consuming post-mortem analysis. We demonstrate our system in the context of real-world attack incidents, and validate it against state-of-the-art alternatives. AMON has been deployed and is currently processing 10Gbps+ live Internet traffic at Merit Network. It is extensible and allows the addition of further statistical and filtering modules for real-time forensics.

cs.NI↗