arXiv subjects

Devavrat Shah

Publications and source records attributed to Devavrat Shah.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2024

Integrating Expert Judgment and Algorithmic Decision Making: An Indistinguishability Framework

We introduce a novel framework for human-AI collaboration in prediction and decision tasks. Our approach leverages human judgment to distinguish inputs which are algorithmically indistinguishable, or "look the same" to any feasible predictive algorithm. We argue that this framing clarifies the problem of human-AI collaboration in prediction and decision 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 demonstrate the utility of our framework in a case study of emergency room triage decisions, where we find that although algorithmic risk scores are highly competitive with physicians, there is strong evidence that physician judgments provide signal which could not be replicated by any predictive algorithm. This insight yields a range of natural decision rules which leverage the complementary strengths of human experts and predictive algorithms.

cs.LG↗

arXiv2024

Estimating Ground Reaction Forces from Inertial Sensors

Objective: Our aim is to determine if data collected with inertial measurement units (IMUs) during steady-state running could be used to estimate ground reaction forces (GRFs) and to derive biomechanical variables (e.g., contact time, impulse, change in velocity) using lightweight machine-learning approaches. In contrast, state-of-the-art estimation using LSTMs suffers from prohibitive inference times on edge devices, requires expensive training and hyperparameter optimization, and results in black box models. Methods: We proposed a novel lightweight solution, SVD Embedding Regression (SER), using linear regression between SVD embeddings of IMU data and GRF data. We also compared lightweight solutions including SER and k-Nearest-Neighbors (KNN) regression with state-of-the-art LSTMs. Results: We performed extensive experiments to evaluate these techniques under multiple scenarios and combinations of IMU signals and quantified estimation errors for predicting GRFs and biomechanical variables. We did this using training data from different athletes, from the same athlete, or both, and we explored the use of acceleration and angular velocity data from sensors at different locations (sacrum and shanks). Conclusion: Our results illustrated that lightweight solutions such as SER and KNN can be similarly accurate or more accurate than LSTMs. The use of personal data reduced estimation errors of all methods, particularly for most biomechanical variables (as compared to GRFs); moreover, this gain was more pronounced in the lightweight methods. Significance: The study of GRFs is used to characterize the mechanical loading experienced by individuals in movements such as running, which is clinically applicable to identify athletes at risk for stress-related injuries.

cs.LG↗

arXiv2024

Synthetic Interventions

The synthetic controls (SC) methodology is a prominent tool for policy evaluation in panel data applications. Researchers commonly justify the SC framework with a low-rank matrix factor model that assumes the potential outcomes are described by low-dimensional unit and time specific latent factors. In the recent work of [Abadie '20], one of the pioneering authors of the SC method posed the question of how the SC framework can be extended to multiple treatments. This article offers one resolution to this open question that we call synthetic interventions (SI). Fundamental to the SI framework is a low-rank tensor factor model, which extends the matrix factor model by including a latent factorization over treatments. Under this model, we propose a generalization of the standard SC-based estimators. We prove the consistency for one instantiation of our approach and provide conditions under which it is asymptotically normal. Moreover, we conduct a representative simulation to study its prediction performance and revisit the canonical SC case study of [Abadie-Diamond-Hainmueller '10] on the impact of anti-tobacco legislations by exploring related questions not previously investigated.

econ.EM↗

arXiv2024

Personalized Predictions from Population Level Experiments: A Study on Alzheimer's Disease

The purpose of this article is to infer patient level outcomes from population level randomized control trials (RCTs). In this pursuit, we utilize the recently proposed synthetic nearest neighbors (SNN) estimator. At its core, SNN leverages information across patients to impute missing data associated with each patient of interest. We focus on two types of missing data: (i) unrecorded outcomes from discontinuing the assigned treatments and (ii) unobserved outcomes associated with unassigned treatments. Data imputation in the former powers and de-biases RCTs, while data imputation in the latter simulates "synthetic RCTs" to predict the outcomes for each patient under every treatment. The SNN estimator is interpretable, transparent, and causally justified under a broad class of missing data scenarios. Relative to several standard methods, we empirically find that SNN performs well for the above two applications using Phase 3 clinical trial data on patients with Alzheimer's Disease. Our findings directly suggest that SNN can tackle a current pain point within the clinical trial workflow on patient dropouts and serve as a new tool towards the development of precision medicine. Building on our insights, we discuss how SNN can further generalize to real-world applications.

stat.AP↗

arXiv2024

A Causal Framework to Evaluate Racial Bias in Law Enforcement Systems

We are interested in developing a data-driven method to evaluate race-induced biases in law enforcement systems. While the recent works have addressed this question in the context of police-civilian interactions using police stop data, they have two key limitations. First, bias can only be properly quantified if true criminality is accounted for in addition to race, but it is absent in prior works. Second, law enforcement systems are multi-stage and hence it is important to isolate the true source of bias within the "causal chain of interactions" rather than simply focusing on the end outcome; this can help guide reforms. In this work, we address these challenges by presenting a multi-stage causal framework incorporating criminality. We provide a theoretical characterization and an associated data-driven method to evaluate (a) the presence of any form of racial bias, and (b) if so, the primary source of such a bias in terms of race and criminality. Our framework identifies three canonical scenarios with distinct characteristics: in settings like (1) airport security, the primary source of observed bias against a race is likely to be bias in law enforcement against innocents of that race; (2) AI-empowered policing, the primary source of observed bias against a race is likely to be bias in law enforcement against criminals of that race; and (3) police-civilian interaction, the primary source of observed bias against a race could be bias in law enforcement against that race or bias from the general public in reporting against the other race. Through an extensive empirical study using police-civilian interaction data and 911 call data, we find an instance of such a counter-intuitive phenomenon: in New Orleans, the observed bias is against the majority race and the likely reason for it is the over-reporting (via 911 calls) of incidents involving the minority race by the general public.

stat.AP↗

arXiv2024

Federated Optimization of Smooth Loss Functions

In this work, we study empirical risk minimization (ERM) within a federated learning framework, where a central server minimizes an ERM objective function using training data that is stored across $m$ clients. In this setting, the Federated Averaging (FedAve) algorithm is the staple for determining $ε$-approximate solutions to the ERM problem. Similar to standard optimization algorithms, the convergence analysis of FedAve only relies on smoothness of the loss function in the optimization parameter. However, loss functions are often very smooth in the training data too. To exploit this additional smoothness, we propose the Federated Low Rank Gradient Descent (FedLRGD) algorithm. Since smoothness in data induces an approximate low rank structure on the loss function, our method first performs a few rounds of communication between the server and clients to learn weights that the server can use to approximate clients' gradients. Then, our method solves the ERM problem at the server using inexact gradient descent. To show that FedLRGD can have superior performance to FedAve, we present a notion of federated oracle complexity as a counterpart to canonical oracle complexity. Under some assumptions on the loss function, e.g., strong convexity in parameter, $η$-Hölder smoothness in data, etc., we prove that the federated oracle complexity of FedLRGD scales like $ϕm(p/ε)^{Θ(d/η)}$ and that of FedAve scales like $ϕm(p/ε)^{3/4}$ (neglecting sub-dominant factors), where $ϕ\gg 1$ is a "communication-to-computation ratio," $p$ is the parameter dimension, and $d$ is the data dimension. Then, we show that when $d$ is small and the loss function is sufficiently smooth in the data, FedLRGD beats FedAve in federated oracle complexity. Finally, in the course of analyzing FedLRGD, we also establish a result on low rank approximation of latent variable models.

cs.LG↗

arXiv2023

SAMoSSA: Multivariate Singular Spectrum Analysis with Stochastic Autoregressive Noise

The well-established practice of time series analysis involves estimating deterministic, non-stationary trend and seasonality components followed by learning the residual stochastic, stationary components. Recently, it has been shown that one can learn the deterministic non-stationary components accurately using multivariate Singular Spectrum Analysis (mSSA) in the absence of a correlated stationary component; meanwhile, in the absence of deterministic non-stationary components, the Autoregressive (AR) stationary component can also be learnt readily, e.g. via Ordinary Least Squares (OLS). However, a theoretical underpinning of multi-stage learning algorithms involving both deterministic and stationary components has been absent in the literature despite its pervasiveness. We resolve this open question by establishing desirable theoretical guarantees for a natural two-stage algorithm, where mSSA is first applied to estimate the non-stationary components despite the presence of a correlated stationary AR component, which is subsequently learned from the residual time series. We provide a finite-sample forecasting consistency bound for the proposed algorithm, SAMoSSA, which is data-driven and thus requires minimal parameter tuning. To establish theoretical guarantees, we overcome three hurdles: (i) we characterize the spectra of Page matrices of stable AR processes, thus extending the analysis of mSSA; (ii) we extend the analysis of AR process identification in the presence of arbitrary bounded perturbations; (iii) we characterize the out-of-sample or forecasting error, as opposed to solely considering model identification. Through representative empirical studies, we validate the superior performance of SAMoSSA compared to existing baselines. Notably, SAMoSSA's ability to account for AR noise structure yields improvements ranging from 5% to 37% across various benchmark datasets.

cs.LG↗

arXiv2023

Network Synthetic Interventions: A Causal Framework for Panel Data Under Network Interference

We propose a generalization of the synthetic controls and synthetic interventions methodology to incorporate network interference. We consider the estimation of unit-specific potential outcomes from panel data in the presence of spillover across units and unobserved confounding. Key to our approach is a novel latent factor model that takes into account network interference and generalizes the factor models typically used in panel data settings. We propose an estimator, Network Synthetic Interventions (NSI), and show that it consistently estimates the mean outcomes for a unit under an arbitrary set of counterfactual treatments for the network. We further establish that the estimator is asymptotically normal. We furnish two validity tests for whether the NSI estimator reliably generalizes to produce accurate counterfactual estimates. We provide a novel graph-based experiment design that guarantees the NSI estimator produces accurate counterfactual estimates, and also analyze the sample complexity of the proposed design. We conclude with simulations that corroborate our theoretical findings.

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

On Model Identification and Out-of-Sample Prediction of Principal Component Regression: Applications to Synthetic Controls

We analyze principal component regression (PCR) in a high-dimensional error-in-variables setting with fixed design. Under suitable conditions, we show that PCR consistently identifies the unique model with minimum $\ell_2$-norm. These results enable us to establish non-asymptotic out-of-sample prediction guarantees that improve upon the best known rates. In the course of our analysis, we introduce a natural linear algebraic condition between the in- and out-of-sample covariates, which allows us to avoid distributional assumptions for out-of-sample predictions. Our simulations illustrate the importance of this condition for generalization, even under covariate shifts. Accordingly, we construct a hypothesis test to check when this conditions holds in practice. As a byproduct, our results also lead to novel results for the synthetic controls literature, a leading approach for policy evaluation. To the best of our knowledge, our prediction guarantees for the fixed design setting have been elusive in both the high-dimensional error-in-variables and synthetic controls literatures.

math.ST↗

arXiv2023

Matrix Estimation for Individual Fairness

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

cs.LG↗

arXiv2023

Causal Imputation via Synthetic Interventions

Consider the problem of determining the effect of a compound on a specific cell type. To answer this question, researchers traditionally need to run an experiment applying the drug of interest to that cell type. This approach is not scalable: given a large number of different actions (compounds) and a large number of different contexts (cell types), it is infeasible to run an experiment for every action-context pair. In such cases, one would ideally like to predict the outcome for every pair while only having to perform experiments on a small subset of pairs. This task, which we label "causal imputation", is a generalization of the causal transportability problem. To address this challenge, we extend the recently introduced synthetic interventions (SI) estimator to handle more general data sparsity patterns. We prove that, under a latent factor model, our estimator provides valid estimates for the causal imputation task. We motivate this model by establishing a connection to the linear structural causal model literature. Finally, we consider the prominent CMAP dataset in predicting the effects of compounds on gene expression across cell types. We find that our estimator outperforms standard baselines, thus confirming its utility in biological applications.

stat.ME↗

arXiv2023

Counterfactual Identifiability of Bijective Causal Models

We study counterfactual identifiability in causal models with bijective generation mechanisms (BGM), a class that generalizes several widely-used causal models in the literature. We establish their counterfactual identifiability for three common causal structures with unobserved confounding, and propose a practical learning method that casts learning a BGM as structured generative modeling. Learned BGMs enable efficient counterfactual estimation and can be obtained using a variety of deep conditional generative models. We evaluate our techniques in a visual task and demonstrate its application in a real-world video streaming simulation task.

stat.ML↗

arXiv2023

CausalSim: A Causal Framework for Unbiased Trace-Driven Simulation

We present CausalSim, a causal framework for unbiased trace-driven simulation. Current trace-driven simulators assume that the interventions being simulated (e.g., a new algorithm) would not affect the validity of the traces. However, real-world traces are often biased by the choices algorithms make during trace collection, and hence replaying traces under an intervention may lead to incorrect results. CausalSim addresses this challenge by learning a causal model of the system dynamics and latent factors capturing the underlying system conditions during trace collection. It learns these models using an initial randomized control trial (RCT) under a fixed set of algorithms, and then applies them to remove biases from trace data when simulating new algorithms. Key to CausalSim is mapping unbiased trace-driven simulation to a tensor completion problem with extremely sparse observations. By exploiting a basic distributional invariance property present in RCT data, CausalSim enables a novel tensor completion method despite the sparsity of observations. Our extensive evaluation of CausalSim on both real and synthetic datasets, including more than ten months of real data from the Puffer video streaming system shows it improves simulation accuracy, reducing errors by 53% and 61% on average compared to expert-designed and supervised learning baselines. Moreover, CausalSim provides markedly different insights about ABR algorithms compared to the biased baseline simulator, which we validate with a real deployment.

cs.LG↗

arXiv2023

A User-Driven Framework for Regulating and Auditing Social Media

People form judgments and make decisions based on the information that they observe. A growing portion of that information is not only provided, but carefully curated by social media platforms. Although lawmakers largely agree that platforms should not operate without any oversight, there is little consensus on how to regulate social media. There is consensus, however, that creating a strict, global standard of "acceptable" content is untenable (e.g., in the US, it is incompatible with Section 230 of the Communications Decency Act and the First Amendment). In this work, we propose that algorithmic filtering should be regulated with respect to a flexible, user-driven baseline. We provide a concrete framework for regulating and auditing a social media platform according to such a baseline. In particular, we introduce the notion of a baseline feed: the content that a user would see without filtering (e.g., on Twitter, this could be the chronological timeline). We require that the feeds a platform filters contain "similar" informational content as their respective baseline feeds, and we design a principled way to measure similarity. This approach is motivated by related suggestions that regulations should increase user agency. We present an auditing procedure that checks whether a platform honors this requirement. Notably, the audit needs only black-box access to a platform's filtering algorithm, and it does not access or infer private user information. We provide theoretical guarantees on the strength of the audit. We further show that requiring closeness between filtered and baseline feeds does not impose a large performance cost, nor does it create echo chambers.

cs.CY↗

arXiv2023

Robust Max Entrywise Error Bounds for Tensor Estimation from Sparse Observations via Similarity Based Collaborative Filtering

Consider the task of estimating a 3-order $n \times n \times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. We introduce a similarity based collaborative filtering algorithm for estimating a tensor from sparse observations and argue that it achieves sample complexity that nearly matches the conjectured computationally efficient lower bound on the sample complexity for the setting of low-rank tensors. Our algorithm uses the matrix obtained from the flattened tensor to compute similarity, and estimates the tensor entries using a nearest neighbor estimator. We prove that the algorithm recovers a finite rank tensor with maximum entry-wise error (MEE) and mean-squared-error (MSE) decaying to $0$ as long as each entry is observed independently with probability $p = Ω(n^{-3/2 + κ})$ for any arbitrarily small $κ> 0$. More generally, we establish robustness of the estimator, showing that when arbitrary noise bounded by $\varepsilon \geq 0$ is added to each observation, the estimation error with respect to MEE and MSE degrades by $\text{poly}(\varepsilon)$. Consequently, even if the tensor may not have finite rank but can be approximated within $\varepsilon \geq 0$ by a finite rank tensor, then the estimation error converges to $\text{poly}(\varepsilon)$. Our analysis sheds insight into the conjectured sample complexity lower bound, showing that it matches the connectivity threshold of the graph used by our algorithm for estimating similarity between coordinates.

cs.LG↗