Randomized experiments have become the standard method for companies to evaluate the performance of new products or services. In addition to augmenting managers' decision-making, experimentation mitigates risk by limiting the proportion of customers exposed to innovation. Since many experiments are on customers arriving sequentially, a potential solution is to allow managers to "peek" at the results when new data becomes available and stop the test if the results are statistically significant. Unfortunately, peeking invalidates the statistical guarantees for standard statistical analysis and leads to uncontrolled type-1 error. Our paper provides valid design-based confidence sequences, sequences of confidence intervals with uniform type-1 error guarantees over time for various sequential experiments in an assumption-light manner. In particular, we focus on finite-sample estimands defined on the study participants as a direct measure of the incurred risks by companies. Our proposed confidence sequences are valid for a large class of experiments, including multi-arm bandits, time series, and panel experiments. We further provide a variance reduction technique incorporating modeling assumptions and covariates. Finally, we demonstrate the effectiveness of our proposed approach through a simulation study and three real-world applications from Netflix. Our results show that by using our confidence sequence, harmful experiments could be stopped after only observing a handful of units; for instance, an experiment that Netflix ran on its sign-up page on 30,000 potential customers would have been stopped by our method on the first day before 100 observations.
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Interpreting the inner workings of deep learning models is crucial for establishing trust and ensuring model safety. Concept-based explanations have emerged as a superior approach that is more interpretable than feature attribution estimates such as pixel saliency. However, defining the concepts for the interpretability analysis biases the explanations by the user's expectations on the concepts. To address this, we propose a novel post-hoc unsupervised method that automatically uncovers the concepts learned by deep models during training. By decomposing the latent space of a layer in singular vectors and refining them by unsupervised clustering, we uncover concept vectors aligned with directions of high variance that are relevant to the model prediction, and that point to semantically distinct concepts. Our extensive experiments reveal that the majority of our concepts are readily understandable to humans, exhibit coherency, and bear relevance to the task at hand. Moreover, we showcase the practical utility of our method in dataset exploration, where our concept vectors successfully identify outlier training samples affected by various confounding factors. This novel exploration technique has remarkable versatility to data types and model architectures and it will facilitate the identification of biases and the discovery of sources of error within training data.
In many industrial applications, obtaining labeled observations is not straightforward as it often requires the intervention of human experts or the use of expensive testing equipment. In these circumstances, active learning can be highly beneficial in suggesting the most informative data points to be used when fitting a model. Reducing the number of observations needed for model development alleviates both the computational burden required for training and the operational expenses related to labeling. Online active learning, in particular, is useful in high-volume production processes where the decision about the acquisition of the label for a data point needs to be taken within an extremely short time frame. However, despite the recent efforts to develop online active learning strategies, the behavior of these methods in the presence of outliers has not been thoroughly examined. In this work, we investigate the performance of online active linear regression in contaminated data streams. Our study shows that the currently available query strategies are prone to sample outliers, whose inclusion in the training set eventually degrades the predictive performance of the models. To address this issue, we propose a solution that bounds the search area of a conditional D-optimal algorithm and uses a robust estimator. Our approach strikes a balance between exploring unseen regions of the input space and protecting against outliers. Through numerical simulations, we show that the proposed method is effective in improving the performance of online active learning in the presence of outliers, thus expanding the potential applications of this powerful tool.
Analysis of high-dimensional data, where the number of covariates is larger than the sample size, is a topic of current interest. In such settings, an important goal is to estimate the signal level $\tau^2$ and noise level $\sigma^2$, i.e., to quantify how much variation in the response variable can be explained by the covariates, versus how much of the variation is left unexplained. This thesis considers the estimation of these quantities in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no responses $Y$. Our main research question is: how can one use the unlabeled data to better estimate $\tau^2$ and $\sigma^2$? We consider two frameworks: a linear regression model and a linear projection model in which linearity is not assumed. In the first framework, while linear regression is used, no sparsity assumptions on the coefficients are made. In the second framework, the linearity assumption is also relaxed and we aim to estimate the signal and noise levels defined by the linear projection. We first propose a naive estimator which is unbiased and consistent, under some assumptions, in both frameworks. We then show how the naive estimator can be improved by using zero-estimators, where a zero-estimator is a statistic arising from the unlabeled data, whose expected value is zero. In the first framework, we calculate the optimal zero-estimator improvement and discuss ways to approximate the optimal improvement. In the second framework, such optimality does no longer hold and we suggest two zero-estimators that improve the naive estimator although not necessarily optimally. Furthermore, we show that our approach reduces the variance for general initial estimators and we present an algorithm that potentially improves any initial estimator. Lastly, we consider four datasets and study the performance of our suggested methods.
I consider a class of statistical decision problems in which the policy maker must decide between two alternative policies to maximize social welfare based on a finite sample. The central assumption is that the underlying, possibly infinite-dimensional parameter, lies in a known convex set, potentially leading to partial identification of the welfare effect. An example of such restrictions is the smoothness of counterfactual outcome functions. As the main theoretical result, I derive a finite-sample, exact minimax regret decision rule within the class of all decision rules under normal errors with known variance. When the error distribution is unknown, I obtain a feasible decision rule that is asymptotically minimax regret. I apply my results to the problem of whether to change a policy eligibility cutoff in a regression discontinuity setup, and illustrate them in an empirical application to a school construction program in Burkina Faso.
Inference algorithms for probabilistic programming are complex imperative programs with many moving parts. Efficient inference often requires customising an algorithm to a particular probabilistic model or problem, sometimes called inference programming. Most inference frameworks are implemented in languages that lack a disciplined approach to side effects, which can result in monolithic implementations where the structure of the algorithms is obscured and inference programming is hard. Functional programming with typed effects offers a more structured and modular foundation for programmable inference, with monad transformers being the primary structuring mechanism explored to date. This paper presents an alternative approach to inference programming based on algebraic effects. Using effect signatures to specify the key operations of the algorithms, and effect handlers to modularly interpret those operations for specific variants, we develop two abstract algorithms, or inference patterns, representing two important classes of inference: Metropolis-Hastings and particle filtering. We show how our approach reveals the algorithms' high-level structure, and makes it easy to tailor and recombine their parts into new variants. We implement the two inference patterns as a Haskell library, and discuss the pros and cons of algebraic effects vis-a-vis monad transformers as a structuring mechanism for modular imperative algorithm design.
We study the regret of reinforcement learning from offline data generated by a fixed behavior policy in an infinite-horizon discounted Markov decision process (MDP). While existing analyses of common approaches, such as fitted $Q$-iteration (FQI), suggest a $O(1/\sqrt{n})$ convergence for regret, empirical behavior exhibits \emph{much} faster convergence. In this paper, we present a finer regret analysis that exactly characterizes this phenomenon by providing fast rates for the regret convergence. First, we show that given any estimate for the optimal quality function $Q^*$, the regret of the policy it defines converges at a rate given by the exponentiation of the $Q^*$-estimate's pointwise convergence rate, thus speeding it up. The level of exponentiation depends on the level of noise in the \emph{decision-making} problem, rather than the estimation problem. We establish such noise levels for linear and tabular MDPs as examples. Second, we provide new analyses of FQI and Bellman residual minimization to establish the correct pointwise convergence guarantees. As specific cases, our results imply $O(1/n)$ regret rates in linear cases and $\exp(-\Omega(n))$ regret rates in tabular cases. We extend our findings to general function approximation by extending our results to regret guarantees based on $L_p$-convergence rates for estimating $Q^*$ rather than pointwise rates, where $L_2$ guarantees for nonparametric $Q^*$-estimation can be ensured under mild conditions.
Dealing with unjudged documents ("holes") in relevance assessments is a perennial problem when evaluating search systems with offline experiments. Holes can reduce the apparent effectiveness of retrieval systems during evaluation and introduce biases in models trained with incomplete data. In this work, we explore whether large language models can help us fill such holes to improve offline evaluations. We examine an extreme, albeit common, evaluation setting wherein only a single known relevant document per query is available for evaluation. We then explore various approaches for predicting the relevance of unjudged documents with respect to a query and the known relevant document, including nearest neighbor, supervised, and prompting techniques. We find that although the predictions of these One-Shot Labelers (1SL) frequently disagree with human assessments, the labels they produce yield a far more reliable ranking of systems than the single labels do alone. Specifically, the strongest approaches can consistently reach system ranking correlations of over 0.86 with the full rankings over a variety of measures. Meanwhile, the approach substantially increases the reliability of t-tests due to filling holes in relevance assessments, giving researchers more confidence in results they find to be significant. Alongside this work, we release an easy-to-use software package to enable the use of 1SL for evaluation of other ad-hoc collections or systems.
Differential privacy guarantees allow the results of a statistical analysis involving sensitive data to be released without compromising the privacy of any individual taking part. Achieving such guarantees generally requires the injection of noise, either directly into parameter estimates or into the estimation process. Instead of artificially introducing perturbations, sampling from Bayesian posterior distributions has been shown to be a special case of the exponential mechanism, producing consistent, and efficient private estimates without altering the data generative process. The application of current approaches has, however, been limited by their strong bounding assumptions which do not hold for basic models, such as simple linear regressors. To ameliorate this, we propose $\beta$D-Bayes, a posterior sampling scheme from a generalised posterior targeting the minimisation of the $\beta$-divergence between the model and the data generating process. This provides private estimation that is generally applicable without requiring changes to the underlying model and consistently learns the data generating parameter. We show that $\beta$D-Bayes produces more precise inference estimation for the same privacy guarantees, and further facilitates differentially private estimation via posterior sampling for complex classifiers and continuous regression models such as neural networks for the first time.
The state of the art related to parameter correlation in two-parameter models has been reviewed in this paper. The apparent contradictions between the different authors regarding the ability of D--optimality to simultaneously reduce the correlation and the area of the confidence ellipse in two-parameter models were analyzed. Two main approaches were found: 1) those who consider that the optimality criteria simultaneously control the precision and correlation of the parameter estimators; and 2) those that consider a combination of criteria to achieve the same objective. An analytical criterion combining in its structure both the optimality of the precision of the estimators of the parameters and the reduction of the correlation between their estimators is provided. The criterion was tested both in a simple linear regression model, considering all possible design spaces, and in a non-linear model with strong correlation of the estimators of the parameters (Michaelis--Menten) to show its performance. This criterion showed a superior behavior to all the strategies and criteria to control at the same time the precision and the correlation.
Interpretability methods are developed to understand the working mechanisms of black-box models, which is crucial to their responsible deployment. Fulfilling this goal requires both that the explanations generated by these methods are correct and that people can easily and reliably understand them. While the former has been addressed in prior work, the latter is often overlooked, resulting in informal model understanding derived from a handful of local explanations. In this paper, we introduce explanation summary (ExSum), a mathematical framework for quantifying model understanding, and propose metrics for its quality assessment. On two domains, ExSum highlights various limitations in the current practice, helps develop accurate model understanding, and reveals easily overlooked properties of the model. We also connect understandability to other properties of explanations such as human alignment, robustness, and counterfactual minimality and plausibility.
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