arXiv subjects

Moulinath Banerjee

Publications and source records attributed to Moulinath Banerjee.

At least 37 records · Page 2Linked to original sources

arXiv2023

Understanding new tasks through the lens of training data via exponential tilting

Deploying machine learning models to new tasks is a major challenge despite the large size of the modern training datasets. However, it is conceivable that the training data can be reweighted to be more representative of the new (target) task. We consider the problem of reweighing the training samples to gain insights into the distribution of the target task. Specifically, we formulate a distribution shift model based on the exponential tilt assumption and learn train data importance weights minimizing the KL divergence between labeled train and unlabeled target datasets. The learned train data weights can then be used for downstream tasks such as target performance evaluation, fine-tuning, and model selection. We demonstrate the efficacy of our method on Waterbirds and Breeds benchmarks.

cs.LG↗

arXiv2022

Minimax optimal approaches to the label shift problem in non-parametric settings

We study the minimax rates of the label shift problem in non-parametric classification. In addition to the unsupervised setting in which the learner only has access to unlabeled examples from the target domain, we also consider the setting in which a small number of labeled examples from the target domain is available to the learner. Our study reveals a difference in the difficulty of the label shift problem in the two settings, and we attribute this difference to the availability of data from the target domain to estimate the class conditional distributions in the latter setting. We also show that a class proportion estimation approach is minimax rate-optimal in the unsupervised setting.

math.ST↗

arXiv2022

Meta-analysis of heterogeneous data: integrative sparse regression in high-dimensions

We consider the task of meta-analysis in high-dimensional settings in which the data sources are similar but non-identical. To borrow strength across such heterogeneous datasets, we introduce a global parameter that emphasizes interpretability and statistical efficiency in the presence of heterogeneity. We also propose a one-shot estimator of the global parameter that preserves the anonymity of the data sources and converges at a rate that depends on the size of the combined dataset. For high-dimensional linear model settings, we demonstrate the superiority of our identification restrictions in adapting to a previously seen data distribution as well as predicting for a new/unseen data distribution. Finally, we demonstrate the benefits of our approach on a large-scale drug treatment dataset involving several different cancer cell-lines.

stat.ME↗

arXiv2021

A linear adjustment based approach to posterior drift in transfer learning

We present a new model and methods for the posterior drift problem where the regression function in the target domain is modeled as a linear adjustment (on an appropriate scale) of that in the source domain, an idea that inherits the simplicity and the usefulness of generalized linear models and accelerated failure time models from the classical statistics literature, and study the theoretical properties of our proposed estimator in the binary classification problem. Our approach is shown to be flexible and applicable in a variety of statistical settings, and can be adopted to transfer learning problems in various domains including epidemiology, genetics and biomedicine. As a concrete application, we illustrate the power of our approach through mortality prediction for British Asians by borrowing strength from similar data from the larger pool of British Caucasians, using the UK Biobank data.

stat.ME↗

arXiv2021

Estimation of a score-explained non-randomized treatment effect in fixed and high dimensions

Non-randomized treatment effect models are widely used for the assessment of treatment effects in various fields and in particular social science disciplines like political science, psychometry, psychology. More specifically, these are situations where treatment is assigned to an individual based on some of their characteristics (e.g. scholarship is allocated based on merit or antihypertensive treatments are allocated based on blood pressure level) instead of being allocated randomly, as is the case, for example, in randomized clinical trials. Popular methods that have been largely employed till date for estimation of such treatment effects suffer from slow rates of convergence (i.e. slower than $\sqrt{n}$). In this paper, we present a new model coined SCENTS: Score Explained Non-Randomized Treatment Systems, and a corresponding method that allows estimation of the treatment effect at $\sqrt{n}$ rate in the presence of fairly general forms of confoundedness, when the `score' variable on whose basis treatment is assigned can be explained via certain feature measurements of the individuals under study. We show that our estimator is asymptotically normal in general and semi-parametrically efficient under normal errors. We further extend our analysis to high dimensional covariates and propose a $\sqrt n$ consistent and asymptotically normal estimator based on a de-biasing procedure. Our analysis for the high dimensional incarnation can be readily extended to analyze partial linear models in the presence of noisy variables corresponding to the non-linear part of the model, where the noise can be correlated with the variables corresponding to the linear part. We analyze two real datasets via our method and compare our results with those obtained by using previous approaches. We conclude this paper with a discussion on some possible extensions of our approach.

stat.ME↗

arXiv2021

Asymptotic normality of a linear threshold estimator in fixed dimension with near-optimal rate

Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn about this separating hyperplane. Exact likelihood or least squares methods to estimate the thresholding parameter involve an indicator function which make them difficult to optimize and are, therefore, often tackled by using a surrogate loss that uses a smooth approximation to the indicator. In this paper, we demonstrate that the resulting estimator is asymptotically normal with a near optimal rate of convergence: $n^{-1}$ up to a log factor, in both classification and regression thresholding models. This is substantially faster than the currently established convergence rates of smoothed estimators for similar models in the statistics and econometrics literatures. We also present a real-data application of our approach to an environmental data set where $CO_2$ emission is explained in terms of a separating hyperplane defined through per-capita GDP and urban agglomeration.

math.ST↗

arXiv2021

On robust learning in the canonical change point problem under heavy tailed errors in finite and growing dimensions

This paper presents a number of new findings about the canonical change point estimation problem. The first part studies the estimation of a change point on the real line in a simple stump model using the robust Huber estimating function which interpolates between the $\ell_1$ (absolute deviation) and $\ell_2$ (least squares) based criteria. While the $\ell_2$ criterion has been studied extensively, its robust counterparts and in particular, the $\ell_1$ minimization problem have not. We derive the limit distribution of the estimated change point under the Huber estimating function and compare it to that under the $\ell_2$ criterion. Theoretical and empirical studies indicate that it is more profitable to use the Huber estimating function (and in particular, the $\ell_1$ criterion) under heavy tailed errors as it leads to smaller asymptotic confidence intervals at the usual levels compared to the $\ell_2$ criterion. We also compare the $\ell_1$ and $\ell_2$ approaches in a parallel setting, where one has $m$ independent single change point problems and the goal is to control the maximal deviation of the estimated change points from the true values, and establish rigorously that the $\ell_1$ estimation criterion provides a superior rate of convergence to the $\ell_2$, and that this relative advantage is driven by the heaviness of the tail of the error distribution. Finally, we derive minimax optimal rates for the change plane estimation problem in growing dimensions and demonstrate that Huber estimation attains the optimal rate while the $\ell_2$ scheme produces a rate sub-optimal estimator for heavy tailed errors. In the process of deriving our results, we establish a number of properties about the minimizers of compound Binomial and compound Poisson processes which are of independent interest.

math.ST↗

arXiv2021

Inference In High-dimensional Single-Index Models Under Symmetric Designs

The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression parameter is identifiable. We construct estimates of the regression coefficients of interest that are similar to the debiased lasso estimates in the standard linear model and exhibit similar properties: root-n-consistency and asymptotic normality. The procedure completely bypasses the estimation of the unknown link function, which can be extremely challenging depending on the underlying structure of the problem. Furthermore, under Gaussianity, we propose more efficient estimates of the coefficients by expanding the link function in the Hermite polynomial basis. Finally, we illustrate our approach via carefully designed simulation experiments.

math.ST↗

arXiv2020

A semi-parametric model for target localization in distributed systems

Distributed systems serve as a key technological infrastructure for monitoring diverse systems across space and time. Examples of their widespread applications include: precision agriculture, surveillance, ecosystem and physical infrastructure monitoring, animal behavior and tracking, disaster response and recovery to name a few. Such systems comprise of a large number of sensor devices at fixed locations, wherein each individual sensor obtains measurements that are subsequently fused and processed at a central processing node. A key problem for such systems is to detect targets and identify their locations, for which a large body of literature has been developed focusing primarily on employing parametric models for signal attenuation from target to device. In this paper, we adopt a nonparametric approach that only assumes that the signal is nonincreasing as function of the distance between the sensor and the target. We propose a simple tuning parameter free estimator for the target location, namely, the simple score estimator (SSCE). We show that the SSCE is $\sqrt{n}$ consistent and has a Gaussian limit distribution which can be used to construct asymptotic confidence regions for the location of the target. We study the performance of the SSCE through extensive simulations, and finally demonstrate an application to target detection in a video surveillance data set.

stat.ME↗

arXiv2020

Design of $c$-Optimal Experiments for High dimensional Linear Models

We study random designs that minimize the asymptotic variance of a de-biased lasso estimator when a large pool of unlabeled data is available but measuring the corresponding responses is costly. The optimal sampling distribution arises as the solution of a semidefinite program. The improvements in efficiency that result from these optimal designs are demonstrated via simulation experiments.

math.ST↗

arXiv2020

Optimal Linear Discriminators For The Discrete Choice Model In Growing Dimensions

Manski's celebrated maximum score estimator for the discrete choice model, which is an optimal linear discriminator, has been the focus of much investigation in both the econometrics and statistics literatures, but its behavior under growing dimension scenarios largely remains unknown. This paper addresses that gap. Two different cases are considered: $p$ grows with $n$ but at a slow rate, i.e. $p/n \rightarrow 0$; and $p \gg n$ (fast growth). In the binary response model, we recast Manski's score estimation as empirical risk minimization for a classification problem, and derive the $\ell_2$ rate of convergence of the score estimator under a \emph{transition condition} in terms of our margin parameter that calibrates the level of difficulty of the estimation problem. We also establish upper and lower bounds for the minimax $\ell_2$ error in the binary choice model that differ by a logarithmic factor, and construct a minimax-optimal estimator in the slow growth regime. Some extensions to the general case -- the multinomial response model -- are also considered. Last but not least, we use a variety of learning algorithms to compute the maximum score estimator in growing dimensions.

math.ST↗

arXiv2020

Markovian And Non-Markovian Processes with Active Decision Making Strategies For Addressing The COVID-19 Pandemic

We study and predict the evolution of Covid-19 in six US states from the period May 1 through August 31 using a discrete compartment-based model and prescribe active intervention policies, like lockdowns, on the basis of minimizing a loss function, within the broad framework of partially observed Markov decision processes. For each state, Covid-19 data for 40 days (starting from May 1 for two northern states and June 1 for four southern states) are analyzed to estimate the transition probabilities between compartments and other parameters associated with the evolution of the epidemic. These quantities are then used to predict the course of the epidemic in the given state for the next 50 days (test period) under various policy allocations, leading to different values of the loss function over the training horizon. The optimal policy allocation is the one corresponding to the smallest loss. Our analysis shows that none of the six states need lockdowns over the test period, though the no lockdown prescription is to be interpreted with caution: responsible mask use and social distancing of course need to be continued. The caveats involved in modeling epidemic propagation of this sort are discussed at length. A sketch of a non-Markovian formulation of Covid-19 propagation (and more general epidemic propagation) is presented as an attractive avenue for future research in this area.

stat.AP↗

arXiv2020

Two Simple Ways to Learn Individual Fairness Metrics from Data

Individual fairness is an intuitive definition of algorithmic fairness that addresses some of the drawbacks of group fairness. Despite its benefits, it depends on a task specific fair metric that encodes our intuition of what is fair and unfair for the ML task at hand, and the lack of a widely accepted fair metric for many ML tasks is the main barrier to broader adoption of individual fairness. In this paper, we present two simple ways to learn fair metrics from a variety of data types. We show empirically that fair training with the learned metrics leads to improved fairness on three machine learning tasks susceptible to gender and racial biases. We also provide theoretical guarantees on the statistical performance of both approaches.

stat.ML↗

arXiv2020

Change Point Estimation in a Dynamic Stochastic Block Model

We consider the problem of estimating the location of a single change point in a dynamic stochastic block model. We propose two methods of estimating the change point, together with the model parameters. The first employs a least squares criterion function and takes into consideration the full structure of the stochastic block model and is evaluated at each point in time. Hence, as an intermediate step, it requires estimating the community structure based on a clustering algorithm at every time point. The second method comprises of the following two steps: in the first one, a least squares function is used and evaluated at each time point, but ignores the community structures and just considers a random graph generating mechanism exhibiting a change point. Once the change point is identified, in the second step, all network data before and after it are used together with a clustering algorithm to obtain the corresponding community structures and subsequently estimate the generating stochastic block model parameters. A comparison between these two methods is illustrated. Further, for both methods under their respective identifiability and certain additional regularity conditions, we establish rates of convergence and derive the asymptotic distributions of the change point estimators. The results are illustrated on synthetic data.

math.ST↗

arXiv2020

Intelligent sampling for multiple change-points in exceedingly long time series with rate guarantees

Change point estimation in its offline version is traditionally performed by optimizing over the data set of interest, by considering each data point as the true location parameter and computing a data fit criterion. Subsequently, the data point that minimizes the criterion is declared as the change point estimate. For estimating multiple change points, the procedures are analogous in spirit, but significantly more involved in execution. Since change-points are local discontinuities, only data points close to the actual change point provide useful information for estimation, while data points far away are superfluous, to the point where using only a few points close to the true parameter is just as precise as using the full data set. Leveraging this "locality principle", we introduce a two-stage procedure for the problem at hand, which in the 1st stage uses a sparse subsample to obtain pilot estimates of the underlying change points, and in the 2nd stage refines these estimates by sampling densely in appropriately defined neighborhoods around them. We establish that this method achieves the same rate of convergence and even virtually the same asymptotic distribution as the analysis of the full data, while reducing computational complexity to O(N^0.5) time (N being the length of data set), as opposed to at least O(N) time for all current procedures, making it promising for the analysis on exceedingly long data sets with adequately spaced out change points. The main results are established under a signal plus noise model with independent and identically distributed error terms, but extensions to dependent data settings, as well as multiple stage (>2) procedures are also provided. The performance of our procedure -- which is coined "intelligent sampling" -- is illustrated on both synthetic and real Internet data streams.

stat.ME↗

arXiv2019

Change Point Estimation in Panel Data with Temporal and Cross-sectional Dependence

We study the problem of detecting a common change point in large panel data based on a mean shift model, wherein the errors exhibit both temporal and cross-sectional dependence. A least squares based procedure is used to estimate the location of the change point. Further, we establish the convergence rate and obtain the asymptotic distribution of the least squares estimator. The form of the distribution is determined by the behavior of the norm difference of the means before and after the change point. Since the behavior of this norm difference is, a priori, unknown to the practitioner, we also develop a novel data driven adaptive procedure that provides valid confidence intervals for the common change point, without requiring any such knowledge. Numerical work based on synthetic data illustrates the performance of the estimator in finite samples under different settings of temporal and cross-sectional dependence, sample size and number of panels. Finally, we examine an application to financial stock data and discuss the identified change points.

math.ST↗

arXiv2018

A Conversation with Jon Wellner

Jon August Wellner was born in Portland, Oregon, in August 1945. He received his Bachelor's degree from the University of Idaho in 1968 and his PhD degree from the University of Washington in 1975. From 1975 until 1983 he was an Assistant Professor and Associate Professor at the University of Rochester. In 1983 he returned to the University of Washington, and has remained at the UW as a faculty member since that time. Over the course of a long and distinguished career, Jon has made seminal contributions to a variety of areas including empirical processes, semiparametric theory, and shape-constrained inference, and has co-authored a number of extremely influential books. He has been honored as the Le Cam lecturer by both the IMS (2015) and the French Statistical Society (2017). He is a Fellow of the IMS, the ASA, and the AAAS, and an elected member of the International Statistical Institute. He has served as co-Editor of Annals of Statistics (2001--2003) and Editor of Statistical Science (2010--2013), and President of IMS (2016--2017). In 2010 he was made a Knight of the Order of the Netherlands Lion. In his free time, Jon enjoys mountain climbing and backcountry skiing in the Cascades and British Columbia.

stat.OT↗

arXiv2018

Removing the Curse of Superefficiency: an Effective Strategy For Distributed Computing in Isotonic Regression

We propose a strategy for computing the isotonic least-squares estimate of a monotone function in a general regression setting where the data are distributed across different servers and the observations across servers, though independent, can come from heterogeneous sub-populations, thereby violating the identically distributed assumption. Our strategy fixes the super-efficiency phenomenon observed in prior work on distributed computing in the isotonic regression framework, where averaging several isotonic estimates (each computed at a local server) on a central server produces super-efficient estimates that do not replicate the properties of the global isotonic estimator, i.e. the isotonic estimate that would be constructed by transferring all the data to a single server. The new estimator proposed in this paper works by smoothing the data on each local server, communicating the smoothed summaries to the central server, and then computing an isotonic estimate at the central server, and is shown to replicate the asymptotic properties of the global estimator, and also overcome the super-efficiency phenomenon exhibited by earlier estimators. For data on $N$ observations, the new estimator can be constructed by transferring data just over order $N^{1/3}$ across servers [as compared to transferring data of order $N$ to compute the global isotonic estimator], and requires the same order of computing time as the global estimator.

math.ST↗