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.

Exploiting Exogenous Structure for Sample-Efficient Reinforcement Learning

We study a class of structured Markov Decision Processes (MDPs) known as Exo-MDPs, characterized by a partition of the state space into two components. The exogenous states evolve stochastically in a manner not affected by the agent's actions, whereas the endogenous states are affected by the actions, and evolve in a deterministic and known way conditional on the exogenous states. Exo-MDPs are a natural model for various applications including inventory control, finance, power systems, ride sharing, among others. Despite seeming restrictive, this work establishes that any discrete MDP can be represented as an Exo-MDP. Further, Exo-MDPs induce a natural representation of the transition and reward dynamics as linear functions of the exogenous state distribution. This linear representation leads to near-optimal algorithms with regret guarantees scaling only with the (effective) size of the exogenous state space $d$, independent of the sizes of the endogenous state and action spaces. Specifically, when the exogenous state is fully observed, a simple plug-in approach achieves a regret upper bound of $O(H^{3/2}\sqrt{dK})$, where $H$ denotes the horizon and $K$ denotes the total number of episodes. When the exogenous state is unobserved, the linear representation leads to a regret upper bound of $O(H^{3/2}d\sqrt{K})$. We also establish a nearly matching regret lower bound of $\Omega(Hd\sqrt{K})$ for the no observation regime. We complement our theoretical findings with an experimental study on inventory control problems.

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.

Distinguishing the Indistinguishable: Human Expertise in Algorithmic Prediction

We introduce a novel framework for incorporating human expertise into algorithmic predictions. Our approach focuses on the use of human judgment to distinguish inputs which `look the same' to any feasible predictive algorithm. We argue that this framing clarifies the problem of human/AI collaboration in prediction tasks, as experts often have access to information -- particularly subjective information -- which is not encoded in the algorithm's training data. We use this insight to develop a set of principled algorithms for selectively incorporating human feedback only when it improves the performance of any feasible predictor. We find empirically that although algorithms often outperform their human counterparts on average, human judgment can significantly 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.

Predicting Ground Reaction Force from Inertial Sensors

The study of ground reaction forces (GRF) 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. Our aim in this paper is to determine if data collected with inertial measurement units (IMUs), that can be worn by athletes during outdoor runs, can be used to predict GRF with sufficient accuracy to allow the analysis of its derived biomechanical variables (e.g., contact time and loading rate). In this paper, we consider lightweight approaches in contrast to state-of-the-art prediction using LSTM neural networks. Specifically, we compare use of LSTMs to k-Nearest Neighbors (KNN) regression as well as propose a novel solution, SVD Embedding Regression (SER), using linear regression between singular value decomposition embeddings of IMUs data (input) and GRF data (output). We evaluate the accuracy of these techniques when using training data collected from different athletes, from the same athlete, or both, and we explore the use of acceleration and angular velocity data from sensors at different locations (sacrum and shanks). Our results illustrate that simple machine learning methods such as SER and KNN can be similarly accurate or more accurate than LSTM neural networks, with much faster training times and hyperparameter optimization; in particular, SER and KNN are more accurate when personal training data are available, and KNN comes with benefit of providing provenance of prediction. Notably, the use of personal data reduces prediction errors of all methods for most biomechanical variables.

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 $\alpha$ in the parameter estimation with sample complexity $O({\sf poly}(k)/\alpha^2)$. Our method achives the order-optimal sample complexity of $O({\sf log}(k)/\alpha^2)$ when tailored for node-wise-sparse Markov random fields. Finally, we demonstrate the performance of our estimator via numerical experiments.

Exploiting Observation Bias to Improve Matrix Completion

We consider a variant of matrix completion where entries are revealed in a biased manner, adopting a model akin to that introduced by Ma and Chen. Instead of treating this observation bias as a disadvantage, as is typically the case, our goal is to exploit the shared information between the bias and the outcome of interest to improve predictions. Towards this, we propose a simple two-stage algorithm: (i) interpreting the observation pattern as a fully observed noisy matrix, we apply traditional matrix completion methods to the observation pattern to estimate the distances between the latent factors; (ii) we apply supervised learning on the recovered features to impute missing observations. We establish finite-sample error rates that are competitive with the corresponding supervised learning parametric rates, suggesting that our learning performance is comparable to having access to the unobserved covariates. Empirical evaluation using a real-world dataset reflects similar performance gains, with our algorithm's estimates having 30x smaller mean squared error compared to traditional matrix completion methods.

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 not captured in 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.

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.

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.