arXiv subjects

Abhin Shah

Publications and source records attributed to Abhin Shah.

13 recordsLinked to original sources

arXiv2025

A Unified View on Learning Unnormalized Distributions via Noise-Contrastive Estimation

This paper studies a family of estimators based on noise-contrastive estimation (NCE) for learning unnormalized distributions. The main contribution of this work is to provide a unified perspective on various methods for learning unnormalized distributions, which have been independently proposed and studied in separate research communities, through the lens of NCE. This unified view offers new insights into existing estimators. Specifically, for exponential families, we establish the finite-sample convergence rates of the proposed estimators under a set of regularity assumptions, most of which are new.

stat.ML↗

arXiv2024

Doubly Robust Inference in Causal Latent Factor Models

This article introduces a new estimator of average treatment effects under unobserved confounding in modern data-rich environments featuring large numbers of units and outcomes. The proposed estimator is doubly robust, combining outcome imputation, inverse probability weighting, and a novel cross-fitting procedure for matrix completion. We derive finite-sample and asymptotic guarantees, and show that the error of the new estimator converges to a mean-zero Gaussian distribution at a parametric rate. Simulation results demonstrate the relevance of the formal properties of the estimators analyzed in this article.

econ.EM↗

arXiv2023

On counterfactual inference with unobserved confounding

Given an observational study with $n$ independent but heterogeneous units, our goal is to learn the counterfactual distribution for each unit using only one $p$-dimensional sample per unit containing covariates, interventions, and outcomes. Specifically, we allow for unobserved confounding that introduces statistical biases between interventions and outcomes as well as exacerbates the heterogeneity across units. Modeling the conditional distribution of the outcomes as an exponential family, we reduce learning the unit-level counterfactual distributions to learning $n$ exponential family distributions with heterogeneous parameters and only one sample per distribution. We introduce a convex objective that pools all $n$ samples to jointly learn all $n$ parameter vectors, and provide a unit-wise mean squared error bound that scales linearly with the metric entropy of the parameter space. For example, when the parameters are $s$-sparse linear combination of $k$ known vectors, the error is $O(s\log k/p)$. En route, we derive sufficient conditions for compactly supported distributions to satisfy the logarithmic Sobolev inequality. As an application of the framework, our results enable consistent imputation of sparsely missing covariates.

cs.LG↗

arXiv2023

On Computationally Efficient Learning of Exponential Family Distributions

We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the natural parameters are appropriately bounded. While the traditional maximum likelihood estimator for this class of exponential family is consistent, asymptotically normal, and asymptotically efficient, evaluating it is computationally hard. In this work, we propose a novel loss function and a computationally efficient estimator that is consistent as well as asymptotically normal under mild conditions. We show that, at the population level, our method can be viewed as the maximum likelihood estimation of a re-parameterized distribution belonging to the same class of exponential family. Further, we show that our estimator can be interpreted as a solution to minimizing a particular Bregman score as well as an instance of minimizing the \textit{surrogate} likelihood. We also provide finite sample guarantees to achieve an error (in $\ell_2$-norm) of $α$ in the parameter estimation with sample complexity $O({\sf poly}(k)/α^2)$. Our method achives the order-optimal sample complexity of $O({\sf log}(k)/α^2)$ when tailored for node-wise-sparse Markov random fields. Finally, we demonstrate the performance of our estimator via numerical experiments.

cs.LG↗

arXiv2023

Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge

Causal effect estimation from data typically requires assumptions about the cause-effect relations either explicitly in the form of a causal graph structure within the Pearlian framework, or implicitly in terms of (conditional) independence statements between counterfactual variables within the potential outcomes framework. When the treatment variable and the outcome variable are confounded, front-door adjustment is an important special case where, given the graph, causal effect of the treatment on the target can be estimated using post-treatment variables. However, the exact formula for front-door adjustment depends on the structure of the graph, which is difficult to learn in practice. In this work, we provide testable conditional independence statements to compute the causal effect using front-door-like adjustment without knowing the graph under limited structural side information. We show that our method is applicable in scenarios where knowing the Markov equivalence class is not sufficient for causal effect estimation. We demonstrate the effectiveness of our method on a class of random graphs as well as real causal fairness benchmarks.

cs.LG↗

arXiv2023

Group Fairness with Uncertainty in Sensitive Attributes

Learning a fair predictive model is crucial to mitigate biased decisions against minority groups in high-stakes applications. A common approach to learn such a model involves solving an optimization problem that maximizes the predictive power of the model under an appropriate group fairness constraint. However, in practice, sensitive attributes are often missing or noisy resulting in uncertainty. We demonstrate that solely enforcing fairness constraints on uncertain sensitive attributes can fall significantly short in achieving the level of fairness of models trained without uncertainty. To overcome this limitation, we propose a bootstrap-based algorithm that achieves the target level of fairness despite the uncertainty in sensitive attributes. The algorithm is guided by a Gaussian analysis for the independence notion of fairness where we propose a robust quadratically constrained quadratic problem to ensure a strict fairness guarantee with uncertain sensitive attributes. Our algorithm is applicable to both discrete and continuous sensitive attributes and is effective in real-world classification and regression tasks for various group fairness notions, e.g., independence and separation.

cs.LG↗

arXiv2022

Selective Regression Under Fairness Criteria

Selective regression allows abstention from prediction if the confidence to make an accurate prediction is not sufficient. In general, by allowing a reject option, one expects the performance of a regression model to increase at the cost of reducing coverage (i.e., by predicting on fewer samples). However, as we show, in some cases, the performance of a minority subgroup can decrease while we reduce the coverage, and thus selective regression can magnify disparities between different sensitive subgroups. Motivated by these disparities, we propose new fairness criteria for selective regression requiring the performance of every subgroup to improve with a decrease in coverage. We prove that if a feature representation satisfies the sufficiency criterion or is calibrated for mean and variance, than the proposed fairness criteria is met. Further, we introduce two approaches to mitigate the performance disparity across subgroups: (a) by regularizing an upper bound of conditional mutual information under a Gaussian assumption and (b) by regularizing a contrastive loss for conditional mean and conditional variance prediction. The effectiveness of these approaches is demonstrated on synthetic and real-world datasets.

cs.LG↗

arXiv2022

Optimal Compression of Locally Differentially Private Mechanisms

Compressing the output of ε-locally differentially private (LDP) randomizers naively leads to suboptimal utility. In this work, we demonstrate the benefits of using schemes that jointly compress and privatize the data using shared randomness. In particular, we investigate a family of schemes based on Minimal Random Coding (Havasi et al., 2019) and prove that they offer optimal privacy-accuracy-communication tradeoffs. Our theoretical and empirical findings show that our approach can compress PrivUnit (Bhowmick et al., 2018) and Subset Selection (Ye et al., 2018), the best known LDP algorithms for mean and frequency estimation, to to the order of ε-bits of communication while preserving their privacy and accuracy guarantees.

cs.CR↗

arXiv2022

Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledge

Treatment effect estimation from observational data is a fundamental problem in causal inference. There are two very different schools of thought that have tackled this problem. On one hand, Pearlian framework commonly assumes structural knowledge (provided by an expert) in form of directed acyclic graphs and provides graphical criteria such as back-door criterion to identify valid adjustment sets. On other hand, potential outcomes (PO) framework commonly assumes that all observed features satisfy ignorability (i.e., no hidden confounding), which in general is untestable. In prior works that attempted to bridge these frameworks, there is an observational criteria to identify an anchor variable and if a subset of covariates (not involving the anchor variable) passes a suitable conditional independence criteria, then that subset is a valid back-door. Our main result strengthens these prior results by showing that under a different expert-driven structural knowledge -- that one variable is a direct causal parent of treatment variable -- remarkably, testing for subsets (not involving the known parent variable) that are valid back-doors is equivalent to an invariance test. Importantly, we also cover the non-trivial case where entire set of observed features is not ignorable (generalizing the PO framework) without requiring knowledge of all parents of treatment variable. Our key technical idea involves generation of a synthetic sub-sampling (or environment) variable that is a function of the known parent variable. In addition to designing an invariance test, this sub-sampling variable allows us to leverage Invariant Risk Minimization, and thus, connects finding valid adjustments (in non-ignorable observational setting) to representation learning. We demonstrate effectiveness and tradeoffs of our approaches on a variety of synthetic data as well as real causal effect estimation benchmarks.

cs.LG↗

arXiv2021

A Computationally Efficient Method for Learning Exponential Family Distributions

We consider the question of learning the natural parameters of a $k$ parameter minimal exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the natural parameters are appropriately bounded. While the traditional maximum likelihood estimator for this class of exponential family is consistent, asymptotically normal, and asymptotically efficient, evaluating it is computationally hard. In this work, we propose a computationally efficient estimator that is consistent as well as asymptotically normal under mild conditions. We provide finite sample guarantees to achieve an ($\ell_2$) error of $α$ in the parameter estimation with sample complexity $O(\mathrm{poly}(k/α))$ and computational complexity ${O}(\mathrm{poly}(k/α))$. To establish these results, we show that, at the population level, our method can be viewed as the maximum likelihood estimation of a re-parameterized distribution belonging to the same class of exponential family.

cs.LG↗

arXiv2021

Treatment Effect Estimation using Invariant Risk Minimization

Inferring causal individual treatment effect (ITE) from observational data is a challenging problem whose difficulty is exacerbated by the presence of treatment assignment bias. In this work, we propose a new way to estimate the ITE using the domain generalization framework of invariant risk minimization (IRM). IRM uses data from multiple domains, learns predictors that do not exploit spurious domain-dependent factors, and generalizes better to unseen domains. We propose an IRM-based ITE estimator aimed at tackling treatment assignment bias when there is little support overlap between the control group and the treatment group. We accomplish this by creating diversity: given a single dataset, we split the data into multiple domains artificially. These diverse domains are then exploited by IRM to more effectively generalize regression-based models to data regions that lack support overlap. We show gains over classical regression approaches to ITE estimation in settings when support mismatch is more pronounced.

cs.LG↗

arXiv2020

On Learning Continuous Pairwise Markov Random Fields

We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed in Vuffray et al. (2019) can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression a` la Lasso, which may be of interest in its own right.

cs.LG↗

arXiv2017

Classical information driven quantum dot thermal machines

We analyze the transient response of quantum dot thermal machines that can be driven by hyperfine interaction acting as a source of classical information. Our setup comprises a quantum dot coupled to two contacts that drive heat flow while coupled to a nuclear spin bath. The quantum dot thermal machines operate both as batteries and as engines, depending on the parameter range. The electrons in the quantum dot interact with the nuclear spins via hyperfine spin-flip processes as typically seen in solid state systems such as GaAs quantum dots. The hyperfine interaction in such systems, which is often treated as a deterrent for quantum information processing, can favorably be regarded as a driving agent for classical information flow into a heat engine setup. We relate this information flow to Landauer's erasure of the nuclear spin bath, leading to a battery operation. We further demonstrate that the setup can perform as a transient power source even under a voltage bias across the dot. Focusing on the transient thermoelectric operation, our analysis clearly indicates the role of Landauer's erasure to deliver a higher output power than a conventional quantum dot thermoelectric setup and an efficiency greater than that of an identical Carnot cycle in steady state, which is consistent with recently proposed bounds on efficiency for systems subject to a feedback controller. The role of nuclear spin relaxation processes on these aspects is also studied. Finally, we introduce the Coulomb interaction in the dot and analyze the transient thermoelectric response of the system. Our results elaborate on the effective use of somewhat undesirable scattering processes as a non-equilibrium source of Shannon information flow in thermal machines and the possibilities that may arise from the use of a quantum information source.

cond-mat.mes-hall↗