arXiv subjects

Devavrat Shah

Publications and source records attributed to Devavrat Shah.

At least 19 recordsLinked to original sources

arXiv2026

Synthetic Nearest Neighbors: Extending Synthetic Controls for Matrix Completion with Missing Not at Random Data

We develop a causal framework for matrix completion under missing not at random (MNAR) data. Drawing on synthetic controls from the econometric panel data literature, our approach relaxes two assumptions common in MNAR matrix completion: positivity and independence of observation indicators. Unlike traditional panel data models, which often require prescribed block-sparse geometries, our framework accommodates flexible, heterogeneous observation patterns through target-specific local information structures. We propose synthetic nearest neighbors (SNN), a local synthetic-controls-inspired estimator, and establish finite-sample entrywise error bounds and consistency for mean recovery under suitable conditions. We further derive asymptotic normality under heteroskedastic noise and develop feasible entrywise inference. To estimate entry-specific noise variances, we apply the same local principle to squared outcomes, obtaining consistency under bounded noise and asymptotic unbiasedness under general subgaussian noise. Simulation studies corroborate the theoretical findings across a range of missingness designs and observation patterns.

stat.ME↗

arXiv2026

Doubly robust nearest neighbors in factor models

We introduce and analyze an improved variant of nearest neighbors (NN) for estimation with missing data in latent factor models. We consider a matrix completion problem with missing data, where the $(i, t)$-th entry, when observed, is given by its mean $f(u_i, v_t)$ plus mean-zero noise for an unknown function $f$ and latent factors $u_i$ and $v_t$. Prior NN strategies, like unit-unit NN, for estimating the mean $f(u_i, v_t)$ relies on existence of other rows $j$ with $u_j \approx u_i$. Similarly, time-time NN strategy relies on existence of columns $t'$ with $v_{t'} \approx v_t$. These strategies provide poor performance respectively when similar rows or similar columns are not available. Our estimate is doubly robust to this deficit in two ways: (1) As long as there exist either good row or good column neighbors, our estimate provides a consistent estimate. (2) Furthermore, if both good row and good column neighbors exist, it provides a (near-)quadratic improvement in the non-asymptotic error and admits a significantly narrower asymptotic confidence interval when compared to both unit-unit or time-time NN.

stat.ML↗

arXiv2026

Multi-Objective LQR with Linear Scalarization

We study finite approximation of the Pareto front for the multi-objective linear quadratic regulator (LQR). Classical results characterize Pareto-optimal controllers through weighted sums of the objectives, but do not quantify the effect of discretizing the scalarization weights. We prove the needed sensitivity property, showing that an $ε$ perturbation of the weights changes the full objective vector by $O(ε)$. Consequently, computing optimal controls over a finite grid of the weight simplex uniformly approximates the Pareto front. We also extend the guarantee to unknown dynamics via certainty equivalence, showing that if the model estimates are accurate to the target accuracy, the same procedure stabilizes the true system and attains the same Pareto-front guarantee.

math.OC↗

arXiv2026

On Multivariate Singular Spectrum Analysis: Tensor and Matrix Variants

We introduce and analyze two extensions of Singular Spectrum Analysis (SSA) to the multivariate setting: a new variant of the well-known matrix-based method (mSSA), and a novel tensor-based approach (tSSA). For mSSA, under a spatio-temporal factor model with $N$ time series and $T$ observations per series, we establish that prediction mean-squared-error for both imputation and out-of-sample forecasting effectively scales as $1 / \sqrt{\min(N, T )T}$. This improves over: (i) $1 /\sqrt{T}$ error scaling of SSA, the univariate restriction of mSSA; (ii) $1/\min(N, T)$ error scaling for matrix estimation methods that ignore temporal structure. The out-of-sample forecasting result of mSSA could be of independent interest for online learning under a spatio-temporal factor model. For tSSA, we characterize its imputation mean-squared-error and showcase its better sample complexity, compared to mSSA, for certain regimes of $N$ and $T$. We establish that our spatio-temporal model admits a broad range of time series dynamics including harmonics, polynomials, differentiable periodic functions, and Holder continuous functions. This is further illustrated via the {\em Hankel Calculus}, which establishes that the set of time series the model represents is closed under component-wise addition and multiplication. Empirically, on benchmark datasets, mSSA performs competitively with state-of-the-art neural-network time series methods (e.g. DeepAR, LSTM) and significantly outperforms classical methods such as vector autoregression (VAR). Consistent with our theory, tSSA achieves improved imputation performance over mSSA in certain regimes of $N$ and $T$. Finally, we introduce and analyze an additional variant of SSA to estimate the time-varying variance of a time series. To our knowledge, this is the first result providing provable finite-sample performance guarantees for this task.

cs.LG↗

arXiv2026

Exploiting Exogenous Structure for Sample-Efficient Reinforcement Learning

We study a structured class of Markov Decision Processes, known as Exo-MDPs, in which the state space is partitioned into exogenous and endogenous components. Exogenous states evolve stochastically, independent of the agent's actions, while endogenous states evolve deterministically based on both state components and actions. Exo-MDPs capture many operations research settings, including inventory control, resource management, and ride-sharing. Our first contribution is structural: we establish a representational equivalence between discrete MDPs, Exo-MDPs, and discrete linear mixture MDPs. Our second contribution is statistical. We characterize the minimax regret of learning in Exo-MDPs when the effective dimension r is small relative to the endogenous state and action spaces. When the exogenous states are unobserved, we prove matching upper and lower regret bounds of order $Θ(Hr \sqrt{K})$ over $K$ episodes of horizon $H$, where $r$ is the effective dimension of the Exo-MDP. When exogenous states are observed, the minimax regret improves to $Θ(H\sqrt{ r K})$, revealing a $Θ(\sqrt{r})$ statistical gap due to observation of the exogenous states. These results show that Exo-MDPs decouple sample complexity from action space and endogenous state space. We validate these insights with experiments on inventory control and resource allocation.

stat.ML↗

arXiv2026

Causal Inference for Sequential Settings under Interference and Latent Confounding

We study causal inference under outcome interference for sequential, observational settings. Specifically, we consider settings where the binary outcomes over N units are Markovian across T time steps. At each time step, the outcomes of N units have dependencies captured through an Ising model; each outcome is also impacted through an external field capturing the effects of its treatment as well as latent confounders. Similar to panel data literature, these latent confounders are modeled to have a low-rank factor structure. Our data is a single sample from this high-dimensional distribution. To estimate causal quantities of interest, we provide a computationally efficient method based on Maximum Pseudo-Likelihood Estimation (MPLE) for learning the model parameters. Under mild assumptions, we establish non-asymptotic consistency for parameter estimation and show this translates to faithful estimation of causal quantities of interest after sampling from the learned model. We demonstrate the efficacy of the method through synthetic experiments as well as a real-world case-study investigating causal effects of vaccine rates on COVID-19 death rates within US counties nationwide.

cs.LG↗

arXiv2026

Causal Inference with Categorical Unobserved Confounder via Mixture Learning

Unobserved confounding is a fundamental challenge for estimating causal effects. To address unobserved confounding, recent literature has turned to two different approaches -- proxy variables and the use of multiple treatments. The first approach, commonly referred to as proximal causal inference, requires proxies to be assigned to specific asymmetric roles: treatment-inducing proxies (negative control exposures), variables that act as common causes of the treatment and outcome, and outcome-inducing proxies (negative control outcomes). In practice, however, identifying variables that satisfy these asymmetric roles can be difficult depending on the application domain. The second approach, commonly referred to as the ``Deconfounder," deals with multiple conditionally independent treatments. There has been limited progress towards developing a consistent estimation method for this setting. As the primary contribution of this work, we establish that causal effects are identifiable in both settings when the unobserved confounder is categorical under suitable conditions. Our approach builds on a mixture learning perspective: we show that the underlying confounding structure can be recovered by identifying the corresponding mixture distribution. We propose an estimation procedure based on tensor decomposition, which allows consistent recovery of the latent structure and comes with non-asymptotic guarantees. Simulation studies and real data experiments demonstrate that the proposed method performs well even with limited data.

stat.ME↗

arXiv2026

OBLIQ-Bench: Exposing Overlooked Bottlenecks in Modern Retrievers with Latent and Implicit Queries

Retrieval benchmarks are increasingly saturating, but we argue that efficient search is far from a solved problem. We identify a class of queries we call oblique, which seek documents that instantiate a latent pattern, like finding all tweets that express an implicit stance, chat logs that demonstrate a particular failure mode, or transcripts that match an abstract scenario. We study three mechanisms through which obliqueness may arise and introduce OBLIQ-Bench, a suite of five oblique search problems over real long-tail corpora. OBLIQ-Bench exposes an overlooked asymmetry between retrieval and verification, where reasoning LLMs reliably recognize latent relevance whenever relevant documents are surfaced, but even sophisticated retrieval pipelines fail to surface most relevant documents in the first place. We hope that OBLIQ-Bench will drive research into retrieval architectures that efficiently capture latent patterns and implicit signals in large corpora.

cs.IR↗

arXiv2025

The Impossibility of Inverse Permutation Learning in Transformer Models

In this technical note, we study the problem of inverse permutation learning in decoder-only transformers. Given a permutation and a string to which that permutation has been applied, the model is tasked with producing the original (``canonical'') string. We argue that this task models a natural robustness property across a variety of reasoning tasks, including long-context retrieval, multiple choice QA and in-context learning. Our primary contribution is an impossibility result: we show that an arbitrary depth, decoder-only transformer cannot learn this task. This result concerns the expressive capacity of decoder-only transformer models and is agnostic to training dynamics or sample complexity. We give a pair of alternative constructions under which inverse permutation learning is feasible. The first of these highlights the fundamental role of the causal attention mask, and reveals a gap between the expressivity of encoder-decoder transformers and the more popular decoder-only architecture. The latter result is more surprising: we show that simply padding the input with ``scratch tokens" yields a construction under which inverse permutation learning is possible. We conjecture that this may suggest an alternative mechanism by which chain-of-thought prompting or, more generally, intermediate ``thinking'' tokens can enable reasoning in large language models, even when these tokens encode no meaningful semantic information (e.g., the results of intermediate computations).

cs.LG↗

arXiv2025

Synthetic Survival Control: Extending Synthetic Controls for "When-If" Decision

Estimating causal effects on time-to-event outcomes from observational data is particularly challenging due to censoring, limited sample sizes, and non-random treatment assignment. The need for answering such "when-if" questions--how the timing of an event would change under a specified intervention--commonly arises in real-world settings with heterogeneous treatment adoption and confounding. To address these challenges, we propose Synthetic Survival Control (SSC) to estimate counterfactual hazard trajectories in a panel data setting where multiple units experience potentially different treatments over multiple periods. In such a setting, SSC estimates the counterfactual hazard trajectory for a unit of interest as a weighted combination of the observed trajectories from other units. To provide formal justification, we introduce a panel framework with a low-rank structure for causal survival analysis. Indeed, such a structure naturally arises under classical parametric survival models. Within this framework, for the causal estimand of interest, we establish identification and finite sample guarantees for SSC. We validate our approach using a multi-country clinical dataset of cancer treatment outcomes, where the staggered introduction of new therapies creates a quasi-experimental setting. Empirically, we find that access to novel treatments is associated with improved survival, as reflected by lower post-intervention hazard trajectories relative to their synthetic counterparts. Given the broad relevance of survival analysis across medicine, economics, and public policy, our framework offers a general and interpretable tool for counterfactual survival inference using observational data.

cs.LG↗

arXiv2025

$k$-SVD with Gradient Descent

The emergence of modern compute infrastructure for iterative optimization has led to great interest in developing optimization-based approaches for a scalable computation of $k$-SVD, i.e., the $k\geq 1$ largest singular values and corresponding vectors of a matrix of rank $d \geq 1$. Despite lots of exciting recent works, all prior works fall short in this pursuit. Specifically, the existing results are either for the exact-parameterized (i.e., $k = d$) and over-parameterized (i.e., $k > d$) settings; or only establish local convergence guarantees; or use a step-size that requires problem-instance-specific oracle-provided information. In this work, we complete this pursuit by providing a gradient-descent method with a simple, universal rule for step-size selection (akin to pre-conditioning), that provably finds $k$-SVD for a matrix of any rank $d \geq 1$. We establish that the gradient method with random initialization enjoys global linear convergence for any $k, d \geq 1$. Our convergence analysis reveals that the gradient method has an attractive region, and within this attractive region, the method behaves like Heron's method (a.k.a. the Babylonian method). Our analytic results about the said attractive region imply that the gradient method can be enhanced by means of Nesterov's momentum-based acceleration technique. The resulting improved convergence rates match those of rather complicated methods typically relying on Lanczos iterations or variants thereof. We provide an empirical study to validate the theoretical results.

cs.LG↗

arXiv2025

Counterfactual inference in sequential experiments

We consider after-study statistical inference for sequentially designed experiments wherein multiple units are assigned treatments for multiple time points using treatment policies that adapt over time. Our goal is to provide inference guarantees for the counterfactual mean at the smallest possible scale -- mean outcome under different treatments for each unit and each time -- with minimal assumptions on the adaptive treatment policy. Without any structural assumptions on the counterfactual means, this challenging task is infeasible due to more unknowns than observed data points. To make progress, we introduce a latent factor model over the counterfactual means that serves as a non-parametric generalization of the non-linear mixed effects model and the bilinear latent factor model considered in prior works. For estimation, we use a non-parametric method, namely a variant of nearest neighbors, and establish a non-asymptotic high probability error bound for the counterfactual mean for each unit and each time. Under regularity conditions, this bound leads to asymptotically valid confidence intervals for the counterfactual mean as the number of units and time points grows to $\infty$ together at suitable rates. We illustrate our theory via several simulations and a case study involving data from a mobile health clinical trial HeartSteps.

stat.ML↗

arXiv2025

Fairness Is More Than Algorithms: Racial Disparities in Time-to-Recidivism

Racial disparities in recidivism remain a persistent challenge within the criminal justice system, increasingly exacerbated by the adoption of algorithmic risk assessment tools. Past works have primarily focused on bias induced by these tools, treating recidivism as a binary outcome. Limited attention has been given to non-algorithmic factors (including socioeconomic ones) in driving racial disparities from a systemic perspective. To that end, this work presents a multi-stage causal framework to investigate the advent and extent of disparities by considering time-to-recidivism rather than a simple binary outcome. The framework captures interactions among races, the algorithm, and contextual factors. This work introduces the notion of counterfactual racial disparity and offers a formal test using survival analysis that can be conducted with observational data to assess if differences in recidivism arise from algorithmic bias, contextual factors, or their interplay. In particular, it is formally established that if sufficient statistical evidence for differences across racial groups is observed, it would support rejecting the null hypothesis that non-algorithmic factors (including socioeconomic ones) do not affect recidivism. An empirical study applying this framework to the COMPAS dataset reveals that short-term recidivism patterns do not exhibit racial disparities when controlling for risk scores. However, statistically significant disparities emerge with longer follow-up periods, particularly for low-risk groups. This suggests that factors beyond algorithmic scores, possibly structural disparities in housing, employment, and social support, may accumulate and exacerbate recidivism risks over time. This underscores the need for policy interventions extending beyond algorithmic improvements to address broader influences on recidivism trajectories.

cs.CY↗

arXiv2025

A Causal Inference Framework for Data Rich Environments

We propose a formal model for counterfactual estimation with unobserved confounding in "data-rich" settings, i.e., where there are a large number of units and a large number of measurements per unit. Our model provides a bridge between the structural causal model view of causal inference common in the graphical models literature with that of the latent factor model view common in the potential outcomes literature. We show how classic models for potential outcomes and treatment assignments fit within our framework. We provide an identification argument for the average treatment effect, the average treatment effect on the treated, and the average treatment effect on the untreated. For any estimator that has a fast enough estimation error rate for a certain nuisance parameter, we establish it is consistent for these various causal parameters. We then show principal component regression is one such estimator that leads to consistent estimation, and we analyze the minimal smoothness required of the potential outcomes function for consistency.

econ.EM↗

arXiv2025

Explaining the Success of Nearest Neighbor Methods in Prediction

Many modern methods for prediction leverage nearest neighbor search to find past training examples most similar to a test example, an idea that dates back in text to at least the 11th century and has stood the test of time. This monograph aims to explain the success of these methods, both in theory, for which we cover foundational nonasymptotic statistical guarantees on nearest-neighbor-based regression and classification, and in practice, for which we gather prominent methods for approximate nearest neighbor search that have been essential to scaling prediction systems reliant on nearest neighbor analysis to handle massive datasets. Furthermore, we discuss connections to learning distances for use with nearest neighbor methods, including how random decision trees and ensemble methods learn nearest neighbor structure, as well as recent developments in crowdsourcing and graphons. In terms of theory, our focus is on nonasymptotic statistical guarantees, which we state in the form of how many training data and what algorithm parameters ensure that a nearest neighbor prediction method achieves a user-specified error tolerance. We begin with the most general of such results for nearest neighbor and related kernel regression and classification in general metric spaces. In such settings in which we assume very little structure, what enables successful prediction is smoothness in the function being estimated for regression, and a low probability of landing near the decision boundary for classification. In practice, these conditions could be difficult to verify for a real dataset. We then cover recent guarantees on nearest neighbor prediction in the three case studies of time series forecasting, recommending products to people over time, and delineating human organs in medical images by looking at image patches. In these case studies, clustering structure enables successful prediction.

cs.LG↗

arXiv2024

Exploiting Observation Bias to Improve Matrix Completion

We consider a variant of matrix completion where entries are revealed in a biased manner. We wish to understand the extent to which such bias can be exploited in improving predictions. Towards that, we propose a natural model where the observation pattern and outcome of interest are driven by the same set of underlying latent (or unobserved) factors. We devise Mask Nearest Neighbor (MNN), a novel two-stage matrix completion algorithm: first, it recovers (distances between) the latent factors by utilizing matrix estimation for the fully observed noisy binary matrix, corresponding to the observation pattern; second, it utilizes the recovered latent factors as features and sparsely observed noisy outcomes as labels to perform non-parametric supervised learning. Our analysis reveals that MNN enjoys entry-wise finite-sample error rates that are competitive with corresponding supervised learning parametric rates. Despite not having access to the latent factors and dealing with biased observations, MNN exhibits such competitive performance via only exploiting the shared information between the bias and outcomes. Finally, through empirical evaluation using a real-world dataset, we find that with MNN, the estimates have 28x smaller mean squared error compared to traditional matrix completion methods, suggesting the utility of the model and method proposed in this work.

cs.LG↗

arXiv2024

Auditing for Human Expertise

High-stakes prediction tasks (e.g., patient diagnosis) are often handled by trained human experts. A common source of concern about automation in these settings is that experts may exercise intuition that is difficult to model and/or have access to information (e.g., conversations with a patient) that is simply unavailable to a would-be algorithm. This raises a natural question whether human experts add value which could not be captured by an algorithmic predictor. We develop a statistical framework under which we can pose this question as a natural hypothesis test. Indeed, as our framework highlights, detecting human expertise is more subtle than simply comparing the accuracy of expert predictions to those made by a particular learning algorithm. Instead, we propose a simple procedure which tests whether expert predictions are statistically independent from the outcomes of interest after conditioning on the available inputs (`features'). A rejection of our test thus suggests that human experts may add value to any algorithm trained on the available data, and has direct implications for whether human-AI `complementarity' is achievable in a given prediction task. We highlight the utility of our procedure using admissions data collected from the emergency department of a large academic hospital system, where we show that physicians' admit/discharge decisions for patients with acute gastrointestinal bleeding (AGIB) appear to be incorporating information that is not available to a standard algorithmic screening tool. This is despite the fact that the screening tool is arguably more accurate than physicians' discretionary decisions, highlighting that -- even absent normative concerns about accountability or interpretability -- accuracy is insufficient to justify algorithmic automation.

stat.ML↗

arXiv2024

Human Expertise in Algorithmic Prediction

We introduce a novel framework for incorporating human expertise into algorithmic predictions. Our approach leverages human judgment to distinguish inputs which are algorithmically indistinguishable, or "look the same" to predictive algorithms. We argue that this framing clarifies the problem of human-AI collaboration in prediction tasks, as experts often form judgments by drawing on information which is not encoded in an algorithm's training data. Algorithmic indistinguishability yields a natural test for assessing whether experts incorporate this kind of "side information", and further provides a simple but principled method for selectively incorporating human feedback into algorithmic predictions. We show that this method provably improves the performance of any feasible algorithmic predictor and precisely quantify this improvement. We find empirically that although algorithms often outperform their human counterparts on average, human judgment can improve algorithmic predictions on specific instances (which can be identified ex-ante). In an X-ray classification task, we find that this subset constitutes nearly $30\%$ of the patient population. Our approach provides a natural way of uncovering this heterogeneity and thus enabling effective human-AI collaboration.

cs.LG↗