Anish K. Agarwal

Keegan Harris, Anish Agarwal, Chara Podimata et al. · harvard

We consider the problem of decision-making using panel data, in which a decision-maker gets noisy, repeated measurements of multiple units (or agents). We consider a setup where there is a pre-intervention period, when the principal observes the outcomes of each unit, after which the principal uses these observations to assign a treatment to each unit. Unlike this classical setting, we permit the units generating the panel data to be strategic, i.e. units may modify their pre-intervention outcomes in order to receive a more desirable intervention. The principal's goal is to design a strategyproof intervention policy, i.e. a policy that assigns units to their utility-maximizing interventions despite their potential strategizing. We first identify a necessary and sufficient condition under which a strategyproof intervention policy exists, and provide a strategyproof mechanism with a simple closed form when one does exist. Along the way, we prove impossibility results for strategic multiclass classification, which may be of independent interest. When there are two interventions, we establish that there always exists a strategyproof mechanism, and provide an algorithm for learning such a mechanism. For three or more interventions, we provide an algorithm for learning a strategyproof mechanism if there exists a sufficiently large gap in the principal's rewards between different interventions. Finally, we empirically evaluate our model using real-world panel data collected from product sales over 18 months. We find that our methods compare favorably to baselines which do not take strategic interactions into consideration, even in the presence of model misspecification.

Abhineet Agarwal, Anish Agarwal, Suhas Vijaykumar · berkeley

Consider a setting where there are $N$ heterogeneous units and $p$ interventions. Our goal is to learn unit-specific potential outcomes for any combination of these $p$ interventions, i.e., $N \times 2^p$ causal parameters. Choosing a combination of interventions is a problem that naturally arises in a variety of applications such as factorial design experiments, recommendation engines, combination therapies in medicine, conjoint analysis, etc. Running $N \times 2^p$ experiments to estimate the various parameters is likely expensive and/or infeasible as $N$ and $p$ grow. Further, with observational data there is likely confounding, i.e., whether or not a unit is seen under a combination is correlated with its potential outcome under that combination. To address these challenges, we propose a novel latent factor model that imposes structure across units (i.e., the matrix of potential outcomes is approximately rank $r$), and combinations of interventions (i.e., the coefficients in the Fourier expansion of the potential outcomes is approximately $s$ sparse). We establish identification for all $N \times 2^p$ parameters despite unobserved confounding. We propose an estimation procedure, Synthetic Combinations, and establish it is finite-sample consistent and asymptotically normal under precise conditions on the observation pattern. Our results imply consistent estimation given $\text{poly}(r) \times \left( N + s^2p\right)$ observations, while previous methods have sample complexity scaling as $\min(N \times s^2p, \ \ \text{poly(r)} \times (N + 2^p))$. We use Synthetic Combinations to propose a data-efficient experimental design. Empirically, Synthetic Combinations outperforms competing approaches on a real-world dataset on movie recommendations. Lastly, we extend our analysis to do causal inference where the intervention is a permutation over $p$ items (e.g., rankings).

Anish Agarwal, Keegan Harris, Justin Whitehouse et al.

Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the first time-uniform finite sample guarantees for (regularized) PCR whenever data is collected adaptively. Since the proof techniques for analyzing PCR in the fixed design setting do not readily extend to the online setting, our results rely on adapting tools from modern martingale concentration to the error-in-variables setting. We demonstrate the usefulness of our bounds by applying them to the domain of panel data, a ubiquitous setting in econometrics and statistics. As our first application, we provide a framework for experiment design in panel data settings when interventions are assigned adaptively. Our framework may be thought of as a generalization of the synthetic control and synthetic interventions frameworks, where data is collected via an adaptive intervention assignment policy. Our second application is a procedure for learning such an intervention assignment policy in a setting where units arrive sequentially to be treated. In addition to providing theoretical performance guarantees (as measured by regret), we show that our method empirically outperforms a baseline which does not leverage error-in-variables regression.

Anish Agarwal, Sukjin Han, Dwaipayan Saha et al.

We propose a generalization of the synthetic control and interventions methods to the setting with dynamic treatment effects. We consider the estimation of unit-specific treatment effects from panel data collected under a general treatment sequence. Here, each unit receives multiple treatments sequentially, according to an adaptive policy that depends on a latent, endogenously time-varying confounding state. Under a low-rank latent factor model assumption, we develop an identification strategy for any unit-specific mean outcome under any sequence of interventions. The latent factor model we propose admits linear time-varying and time-invariant dynamical systems as special cases. Our approach can be viewed as an identification strategy for structural nested mean models -- a widely used framework for dynamic treatment effects -- under a low-rank latent factor assumption on the blip effects. Unlike these models, however, it is more permissive in observational settings, thereby broadening its applicability. Our method, which we term synthetic blip effects, is a backwards induction process in which the blip effect of a treatment at each period and for a target unit is recursively expressed as a linear combination of the blip effects of a group of other units that received the designated treatment. This strategy avoids the combinatorial explosion in the number of units that would otherwise be required by a naive application of prior synthetic control and intervention methods in dynamic treatment settings. We provide estimation algorithms that are easy to implement in practice and yield estimators with desirable properties. Using unique Korean firm-level panel data, we demonstrate how the proposed framework can be used to estimate individualized dynamic treatment effects and to derive optimal treatment allocation rules in the context of financial support for exporting firms.

Anish Agarwal, Sarah H. Cen, Devavrat Shah et al.

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.

Daniel Ngo, Keegan Harris, Anish Agarwal et al.

We consider the setting of synthetic control methods (SCMs), a canonical approach used to estimate the treatment effect on the treated in a panel data setting. We shed light on a frequently overlooked but ubiquitous assumption made in SCMs of "overlap": a treated unit can be written as some combination -- typically, convex or linear combination -- of the units that remain under control. We show that if units select their own interventions, and there is sufficiently large heterogeneity between units that prefer different interventions, overlap will not hold. We address this issue by proposing a framework which incentivizes units with different preferences to take interventions they would not normally consider. Specifically, leveraging tools from information design and online learning, we propose a SCM that incentivizes exploration in panel data settings by providing incentive-compatible intervention recommendations to units. We establish this estimator obtains valid counterfactual estimates without the need for an a priori overlap assumption. We extend our results to the setting of synthetic interventions, where the goal is to produce counterfactual outcomes under all interventions, not just control. Finally, we provide two hypothesis tests for determining whether unit overlap holds for a given panel dataset.

Abdullah Alomar, Pouya Hamadanian, Arash Nasr-Esfahany et al.

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.

Anish Agarwal, Devavrat Shah, Dennis Shen

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.

Anish Agarwal, Abdullah Alomar, Devavrat Shah

We introduce and analyze a variant of multivariate singular spectrum analysis (mSSA), a popular time series method to impute and forecast a multivariate time series. Under a spatio-temporal factor model we introduce, given $N$ time series and $T$ observations per time series, we establish prediction mean-squared-error for both imputation and out-of-sample forecasting effectively scale as $1 / \sqrt{\min(N, T )T}$. This is an improvement over: (i) $1 /\sqrt{T}$ error scaling of SSA, the restriction of mSSA to a univariate time series; (ii) $1/\min(N, T)$ error scaling for matrix estimation methods which do not exploit temporal structure in the data. The spatio-temporal model we introduce includes any finite sum and products of: harmonics, polynomials, differentiable periodic functions, and Holder continuous functions. Our out-of-sample forecasting result could be of independent interest for online learning under a spatio-temporal factor model. Empirically, on benchmark datasets, our variant of 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). Finally, we propose extensions of mSSA: (i) a variant to estimate time-varying variance of a time series; (ii) a tensor variant which has better sample complexity for certain regimes of $N$ and $T$.

Anish Agarwal, Muhammad Jehangir Amjad, Devavrat Shah et al.

We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which states that for a large model class, the transformed time series matrix is (approximately) low-rank. In effect, this generalizes the widely used Singular Spectrum Analysis (SSA) in time series literature, and allows us to establish a rigorous link between time series analysis and matrix estimation. The key to establishing this link is constructing a Page matrix with non-overlapping entries rather than a Hankel matrix as is commonly done in the literature (e.g., SSA). This particular matrix structure allows us to provide finite sample analysis for imputation and prediction, and prove the asymptotic consistency of our method. Another salient feature of our algorithm is that it is model agnostic with respect to both the underlying time dynamics and the noise distribution in the observations. The noise agnostic property of our approach allows us to recover the latent states when only given access to noisy and partial observations a la a Hidden Markov Model; e.g., recovering the time-varying parameter of a Poisson process without knowing that the underlying process is Poisson. Furthermore, since our forecasting algorithm requires regression with noisy features, our approach suggests a matrix estimation based method - coupled with a novel, non-standard matrix estimation error metric - to solve the error-in-variable regression problem, which could be of interest in its own right. Through synthetic and real-world datasets, we demonstrate that our algorithm outperforms standard software packages (including R libraries) in the presence of missing data as well as high levels of noise.

Niangjun Chen, Anish Agarwal, Adam Wierman et al.

Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error model that generalizes prior models in the learning and stochastic control communities, incorporates correlation among prediction errors, and captures the fact that predictions improve as time passes. We prove that achieving sublinear regret and constant competitive ratio for online algorithms requires the use of an unbounded prediction window in adversarial settings, but that under more realistic stochastic prediction error models it is possible to use Averaging Fixed Horizon Control (AFHC) to simultaneously achieve sublinear regret and constant competitive ratio in expectation using only a constant-sized prediction window. Furthermore, we show that the performance of AFHC is tightly concentrated around its mean.