arXiv subjects

Gabriel Ruiz

Publications and source records attributed to Gabriel Ruiz.

9 recordsLinked to original sources

arXiv2024

Sample size planning for conditional counterfactual mean estimation with a K-armed randomized experiment

We cover how to determine a sufficiently large sample size for a $K$-armed randomized experiment in order to estimate conditional counterfactual expectations in data-driven subgroups. The sub-groups can be output by any feature space partitioning algorithm, including as defined by binning users having similar predictive scores or as defined by a learned policy tree. After carefully specifying the inference target, a minimum confidence level, and a maximum margin of error, the key is to turn the original goal into a simultaneous inference problem where the recommended sample size to offset an increased possibility of estimation error is directly related to the number of inferences to be conducted. Given a fixed sample size budget, our result allows us to invert the question to one about the feasible number of treatment arms or partition complexity (e.g. number of decision tree leaves). Using policy trees to learn sub-groups, we evaluate our nominal guarantees on a large publicly-available randomized experiment test data set.

cs.LG↗

arXiv2022

Neuroevolutionary Feature Representations for Causal Inference

Within the field of causal inference, we consider the problem of estimating heterogeneous treatment effects from data. We propose and validate a novel approach for learning feature representations to aid the estimation of the conditional average treatment effect or CATE. Our method focuses on an intermediate layer in a neural network trained to predict the outcome from the features. In contrast to previous approaches that encourage the distribution of representations to be treatment-invariant, we leverage a genetic algorithm that optimizes over representations useful for predicting the outcome to select those less useful for predicting the treatment. This allows us to retain information within the features useful for predicting outcome even if that information may be related to treatment assignment. We validate our method on synthetic examples and illustrate its use on a real life dataset.

stat.ML↗

arXiv2022

High confidence inference on the probability an individual benefits from treatment using experimental or observational data with known propensity scores

We seek to understand the probability an individual benefits from treatment (PIBT), an inestimable quantity that must be bounded in practice. Given the innate uncertainty in the population-level bounds on PIBT, we seek to better understand the margin of error for their estimation in order to discern whether the estimated bounds on PIBT are tight or wide due to random chance or not. Toward this goal, we present guarantees to the estimation of bounds on marginal PIBT, with any threshold of interest, for a randomized experiment setting or an observational setting where propensity scores are known. We also derive results that permit us to understand heterogeneity in PIBT across learnable sub-groups delineated by pre-treatment features. These results can be used to help with formal statistical power analyses and frequentist confidence statements for settings where we are interested in assumption-lean inference on PIBT through the target bounds with minimal computational complexity compared to a bootstrap approach. Through a real data example from a large randomized experiment, we also demonstrate how our results for PIBT can allow us to understand the practical implication and goodness of fit of an estimate for the conditional average treatment effect (CATE), a function of an individual's baseline covariates.

stat.ME↗

arXiv2022

Sequentially learning the topological ordering of causal directed acyclic graphs with likelihood ratio scores

Causal discovery, the learning of causality in a data mining scenario, has been of strong scientific and theoretical interest as a starting point to identify "what causes what?" Contingent on assumptions and a proper learning algorithm, it is sometimes possible to identify and accurately estimate a causal directed acyclic graph (DAG), as opposed to a Markov equivalence class of graphs that gives ambiguity of causal directions. The focus of this paper is in highlighting the identifiability and estimation of DAGs with general error distributions through a general sequential sorting procedure that orders variables one at a time, starting at root nodes, followed by children of the root nodes, and so on until completion. We demonstrate a novel application of this general approach to estimate the topological ordering of a DAG. At each step of the procedure, only simple likelihood ratio scores are calculated on regression residuals to decide the next node to append to the current partial ordering. The computational complexity of our algorithm on a p-node problem is O(pd), where d is the maximum neighborhood size. Under mild assumptions, the population version of our procedure provably identifies a true ordering of the underlying DAG. We provide extensive numerical evidence to demonstrate that this sequential procedure scales to possibly thousands of nodes and works well for high-dimensional data. We accompany these numerical experiments with an application to a single-cell gene expression dataset.

stat.ME↗

arXiv2021

A causal fused lasso for interpretable heterogeneous treatment effects estimation

We propose a novel method for estimating heterogeneous treatment effects based on the fused lasso. By first ordering samples based on the propensity or prognostic score, we match units from the treatment and control groups. We then run the fused lasso to obtain piecewise constant treatment effects with respect to the ordering defined by the score. Similar to the existing methods based on discretizing the score, our methods yield interpretable subgroup effects. However, existing methods fixed the subgroup a priori, but our causal fused lasso forms data-adaptive subgroups. We show that the estimator consistently estimates the treatment effects conditional on the score under very general conditions on the covariates and treatment. We demonstrate the performance of our procedure using extensive experiments that show that it can be interpretable and competitive with state-of-the-art methods.

stat.ME↗

arXiv2018

A method to Suppress Facial Expression in Posed and Spontaneous Videos

We address the problem of suppressing facial expressions in videos because expressions can hinder the retrieval of important information in applications such as face recognition. To achieve this, we present an optical strain suppression method that removes any facial expression without requiring training for a specific expression. For each frame in a video, an optical strain map that provides the strain magnitude value at each pixel is generated; this strain map is then utilized to neutralize the expression by replacing pixels of high strain values with pixels from a reference face frame. Experimental results of testing the method on various expressions namely happiness, sadness, and anger for two publicly available data sets (i.e., BU-4DFE and AM-FED) show the ability of our method in suppressing facial expressions.

cs.CV↗

arXiv2018

Maximum value of the standardized log of odds ratio and celestial mechanics

The odds ratio (OR) is a widely used measure of the effect size in observational research. ORs reflect statistical association between a binary outcome, such as the presence of a health condition, and a binary predictor, such as an exposure to a pollutant. Statistical significance and interval estimates are often computed for the logarithm of OR, ln(OR), and depend on the asymptotic standard error of ln(OR). For a sample of size N, the standard error can be written as a ratio of sigma over square root of N, where sigma is the population standard deviation of ln(OR). The ratio of ln(OR) over sigma is a standardized effect size. Unlike correlation, that is another familiar standardized statistic, the standardized ln(OR) cannot reach values of minus one or one. We find that its maximum possible value is given by the Laplace Limit Constant, (LLC=0.6627...), that appears as a condition in solutions to Kepler equation -- one of the central equations in celestial mechanics. The range of the standardized ln(OR) is bounded by minus LLC to LLC, reaching its maximum for ln(OR)~4.7987. This range has implications for analysis of epidemiological associations, affecting the behavior of the reasonable prior distribution for the standardized ln(OR).

stat.ME↗

arXiv2016

Assessment of P-value variability in the current replicability crisis

Increased availability of data and accessibility of computational tools in recent years have created unprecedented opportunities for scientific research driven by statistical analysis. Inherent limitations of statistics impose constrains on reliability of conclusions drawn from data but misuse of statistical methods is a growing concern. Significance, hypothesis testing and the accompanying P-values are being scrutinized as representing most widely applied and abused practices. One line of critique is that P-values are inherently unfit to fulfill their ostensible role as measures of scientific hypothesis's credibility. It has also been suggested that while P-values may have their role as summary measures of effect, researchers underappreciate the degree of randomness in the P-value. High variability of P-values would suggest that having obtained a small P-value in one study, one is, nevertheless, likely to obtain a much larger P-value in a similarly powered replication study. Thus, "replicability of P-value" is itself questionable. To characterize P-value variability one can use prediction intervals whose endpoints reflect the likely spread of P-values that could have been obtained by a replication study. Unfortunately, the intervals currently in use, the P-intervals, are based on unrealistic implicit assumptions. Namely, P-intervals are constructed with the assumptions that imply substantial chances of encountering large values of effect size in an observational study, which leads to bias. As an alternative to P-intervals, we develop a method that gives researchers flexibility by providing them with the means to control these assumptions. Unlike endpoints of P-intervals, endpoints of our intervals are directly interpreted as probabilistic bounds for replication P-values and are resistant to selection bias contingent upon approximate prior knowledge of the effect size distribution.

q-bio.GN↗

arXiv2016

The more you test, the more you find: Smallest P-values become increasingly enriched with real findings as more tests are conducted

Increasing accessibility of data to researchers makes it possible to conduct massive amounts of statistical testing. Rather than follow a carefully crafted set of scientific hypotheses with statistical analysis, researchers can now test many possible relations and let P-values or other statistical summaries generate hypotheses for them. Genetic epidemiology field is an illustrative case in this paradigm shift. Driven by technological advances, testing a handful of genetic variants in relation to a health outcome has been abandoned in favor of agnostic screening of the entire genome, followed by selection of top hits, e.g., by selection of genetic variants with the smallest association P-values. At the same time, nearly total lack of replication of claimed associations that has been shaming the field turned to a flow of reports whose findings have been robustly replicating. Researchers may have adopted better statistical practices by learning from past failures, but we suggest that a steep increase in the amount of statistical testing itself is an important factor. Regardless of whether statistical significance has been reached, an increased number of tested hypotheses leads to enrichment of smallest P-values with genuine associations. In this study, we quantify how the expected proportion of genuine signals (EPGS) among top hits changes with an increasing number of tests. When the rate of occurrence of genuine signals does not decrease too sharply to zero as more tests are performed, the smallest P-values are increasingly more likely to represent genuine associations in studies with more tests.

q-bio.GN↗