Debiased Distribution Compression

Modern compression methods can summarize a target distribution $\mathbb{P}$ more succinctly than i.i.d. sampling but require access to a low-bias input sequence like a Markov chain converging quickly to $\mathbb{P}$. We introduce a new suite of compression methods suitable for compression with biased input sequences. Given $n$ points targeting the wrong distribution and quadratic time, Stein Kernel Thinning (SKT) returns $\sqrt{n}$ equal-weighted points with $\widetilde{O}(n^{-1/2})$ maximum mean discrepancy (MMD) to $\mathbb {P}$. For larger-scale compression tasks, Low-rank SKT achieves the same feat in sub-quadratic time using an adaptive low-rank debiasing procedure that may be of independent interest. For downstream tasks that support simplex or constant-preserving weights, Stein Recombination and Stein Cholesky achieve even greater parsimony, matching the guarantees of SKT with as few as $\operatorname{poly-log}(n)$ weighted points. Underlying these advances are new guarantees for the quality of simplex-weighted coresets, the spectral decay of kernel matrices, and the covering numbers of Stein kernel Hilbert spaces. In our experiments, our techniques provide succinct and accurate posterior summaries while overcoming biases due to burn-in, approximate Markov chain Monte Carlo, and tempering.

FairPair: A Robust Evaluation of Biases in Language Models through Paired Perturbations

The accurate evaluation of differential treatment in language models to specific groups is critical to ensuring a positive and safe user experience. An ideal evaluation should have the properties of being robust, extendable to new groups or attributes, and being able to capture biases that appear in typical usage (rather than just extreme, rare cases). Relatedly, bias evaluation should surface not only egregious biases but also ones that are subtle and commonplace, such as a likelihood for talking about appearances with regard to women. We present FairPair, an evaluation framework for assessing differential treatment that occurs during ordinary usage. FairPair operates through counterfactual pairs, but crucially, the paired continuations are grounded in the same demographic group, which ensures equivalent comparison. Additionally, unlike prior work, our method factors in the inherent variability that comes from the generation process itself by measuring the sampling variability. We present an evaluation of several commonly used generative models and a qualitative analysis that indicates a preference for discussing family and hobbies with regard to women.

Doubly Robust Inference in Causal Latent Factor Models

This article introduces a new framework for estimating 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 practical relevance of the formal properties of the estimators analyzed in this article.

Did we personalize? Assessing personalization by an online reinforcement learning algorithm using resampling

There is a growing interest in using reinforcement learning (RL) to personalize sequences of treatments in digital health to support users in adopting healthier behaviors. Such sequential decision-making problems involve decisions about when to treat and how to treat based on the user's context (e.g., prior activity level, location, etc.). Online RL is a promising data-driven approach for this problem as it learns based on each user's historical responses and uses that knowledge to personalize these decisions. However, to decide whether the RL algorithm should be included in an ``optimized'' intervention for real-world deployment, we must assess the data evidence indicating that the RL algorithm is actually personalizing the treatments to its users. Due to the stochasticity in the RL algorithm, one may get a false impression that it is learning in certain states and using this learning to provide specific treatments. We use a working definition of personalization and introduce a resampling-based methodology for investigating whether the personalization exhibited by the RL algorithm is an artifact of the RL algorithm stochasticity. We illustrate our methodology with a case study by analyzing the data from a physical activity clinical trial called HeartSteps, which included the use of an online RL algorithm. We demonstrate how our approach enhances data-driven truth-in-advertising of algorithm personalization both across all users as well as within specific users in the study.

Compress Then Test: Powerful Kernel Testing in Near-linear Time

Kernel two-sample testing provides a powerful framework for distinguishing any pair of distributions based on $n$ sample points. However, existing kernel tests either run in $n^2$ time or sacrifice undue power to improve runtime. To address these shortcomings, we introduce Compress Then Test (CTT), a new framework for high-powered kernel testing based on sample compression. CTT cheaply approximates an expensive test by compressing each $n$ point sample into a small but provably high-fidelity coreset. For standard kernels and subexponential distributions, CTT inherits the statistical behavior of a quadratic-time test -- recovering the same optimal detection boundary -- while running in near-linear time. We couple these advances with cheaper permutation testing, justified by new power analyses; improved time-vs.-quality guarantees for low-rank approximation; and a fast aggregation procedure for identifying especially discriminating kernels. In our experiments with real and simulated data, CTT and its extensions provide 20--200x speed-ups over state-of-the-art approximate MMD tests with no loss of power.

Doubly robust nearest neighbors in factor models

In this technical note, we introduce an improved variant of nearest neighbors for counterfactual inference in panel data settings where multiple units are assigned multiple treatments over multiple time points, each sampled with constant probabilities. We call this estimator a doubly robust nearest neighbor estimator and provide a high probability non-asymptotic error bound for the mean parameter corresponding to each unit at each time. Our guarantee shows that the doubly robust estimator provides a (near-)quadratic improvement in the error compared to nearest neighbor estimators analyzed in prior work for these settings.

On counterfactual inference with unobserved confounding

Given an observational study with $n$ independent but heterogeneous units and one $p$-dimensional sample per unit containing covariates, interventions, and outcomes, our goal is to learn the counterfactual distribution for each unit. We consider studies with unobserved confounding which introduces statistical biases between interventions and outcomes as well as exacerbates the heterogeneity across units. Modeling the underlying joint distribution as an exponential family and under suitable conditions, we reduce learning the $n$ 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 $n$ parameters 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.

Counterfactual inference for sequential experimental design

We consider the problem of counterfactual inference in sequentially designed experiments wherein a collection of $\mathbf{N}$ units each undergo a sequence of interventions for $\mathbf{T}$ time periods, based on policies that sequentially adapt over time. Our goal is counterfactual inference, i.e., estimate what would have happened if alternate policies were used, a problem that is inherently challenging due to the heterogeneity in the outcomes across units and time. To tackle this task, we introduce a suitable latent factor model where the potential outcomes are determined by exogenous unit and time level latent factors. Under suitable conditions, we show that it is possible to estimate the missing (potential) outcomes using a simple variant of nearest neighbors. First, assuming a bilinear latent factor model and allowing for an arbitrary adaptive sampling policy, we establish a distribution-free non-asymptotic guarantee for estimating the missing outcome of any unit at any time; under suitable regularity condition, this guarantee implies that our estimator is consistent. Second, for a generic non-parametric latent factor model, we establish that the estimate for the missing outcome of any unit at time $\mathbf{T}$ satisfies a central limit theorem as $\mathbf{T} \to \infty$, under suitable regularity conditions. Finally, en route to establishing this central limit theorem, we establish a non-asymptotic mean-squared-error bound for the estimate of the missing outcome of any unit at time $\mathbf{T}$. Our work extends the recently growing literature on inference with adaptively collected data by allowing for policies that pool across units, and also compliments the matrix completion literature when the entries are revealed sequentially in an arbitrarily dependent manner based on prior observed data.