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Michael A. Newton

Publications and source records attributed to Michael A. Newton.

10 recordsLinked to original sources
arXiv2026

Empirical Bayes Conformal Prediction for Vision and Language Models

Conformal prediction (CP) gives distribution-free coverage for modern vision and language models, but it is often forced to make a ranking decision from a single unstable nonconformity score. Standard CP uses one realization, while average-then-calibrate variants smooth multiple realizations into a point estimate. Both options discard the inconsistency that can help identify whether a candidate is indeed stable. A weak answer can enter the conformal set even if the evidence is not strong, simply because one posterior sample or prompt phrasing made it look strong. But variability can help distinguish a stable signal from noise-driven fluctuations. We describe an empirical Bayes conformal prediction framework that uses $r$-values to convert score variability into an uncertainty informed nonconformity score. The resulting $r$-value estimates how likely a candidate's latent score belongs to the top-ranked group after accounting for both its mean score and its uncertainty. It admits both a closed-form Normal-Normal empirical Bayes estimator and a nonparametric posterior-sampling estimator. Using the $r$-value as the nonconformity score preserves the target conformal coverage while provably reducing the inclusion of high variance false candidates under mild regularity conditions. Across image classification, CLIP-based VLM benchmarks, and LLMs, we show that $r$-value conformal prediction preserves target coverage while improving ranking stability and reducing set size when variability is informative, and reverting to CP-like behavior when variability vanishes.

cs.LG↗
arXiv2022

Random weighting in LASSO regression

We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters $λ_n$ and suitable regularity conditions. The random-weighting methods in view concern repeated optimization of a randomized objective function, motivated by the need for computational approximations to Bayesian posterior sampling. In the context of LASSO regression, we repeatedly assign analyst-drawn random weights to terms in the objective function (including the penalty terms), and optimize to obtain a sample of random-weighting estimators. We show that existing approaches have conditional model selection consistency and conditional asymptotic normality at different growth rates of $λ_n$ as $n \to \infty$. We propose an extension to the available random-weighting methods and establish that the resulting samples attain conditional sparse normality and conditional consistency in a growing-dimension setting. We find that random-weighting has both approximate-Bayesian and sampling-theory interpretations. Finally, we illustrate the proposed methodology via extensive simulation studies and a benchmark data example.

stat.ME↗
arXiv2020

MixTwice: large-scale hypothesis testing for peptide arrays by variance mixing

Peptide microarrays have emerged as a powerful technology in immunoproteomics as they provide a tool to measure the abundance of different antibodies in patient serum samples. The high dimensionality and small sample size of many experiments challenge conventional statistical approaches, including those aiming to control the false discovery rate (FDR). Motivated by limitations in reproducibility and power of current methods, we advance an empirical Bayesian tool that computes local false discovery rate statistics and local false sign rate statistics when provided with data on estimated effects and estimated standard errors from all the measured peptides. As the name suggests, the \verb+MixTwice+ tool involves the estimation of two mixing distributions, one on underlying effects and one on underlying variance parameters. Constrained optimization techniques provide for model fitting of mixing distributions under weak shape constraints (unimodality of the effect distribution). Numerical experiments show that \verb+MixTwice+ can accurately estimate generative parameters and powerfully identify non-null peptides. In a peptide array study of rheumatoid arthritis (RA), \verb+MixTwice+ recovers meaningful peptide markers in one case where the signal is weak, and has strong reproducibility properties in one case where the signal is strong. \verb+MixTwice+ is available as an R software package. \href{https://github.com/wiscstatman/MixTwice}{https://github.com/wiscstatman/MixTwice}

stat.ME↗
arXiv2020

Bayes Optimal Informer Sets for Early-Stage Drug Discovery

An important experimental design problem in early-stage drug discovery is how to prioritize available compounds for testing when very little is known about the target protein. Informer based ranking (IBR) methods address the prioritization problem when the compounds have provided bioactivity data on other potentially relevant targets. An IBR method selects an informer set of compounds, and then prioritizes the remaining compounds on the basis of new bioactivity experiments performed with the informer set on the target. We formalize the problem as a two-stage decision problem and introduce the Bayes Optimal Informer SEt (BOISE) method for its solution. BOISE leverages a flexible model of the initial bioactivity data, a relevant loss function, and effective computational schemes to resolve the two-step design problem. We evaluate BOISE and compare it to other IBR strategies in two retrospective studies, one on protein-kinase inhibition and the other on anti-cancer drug sensitivity. In both empirical settings BOISE exhibits better predictive performance than available methods. It also behaves well with missing data, where methods that use matrix completion show worse predictive performance. We provide an R implementation of BOISE at https://github.com/wiscstatman/esdd/BOISE

stat.ME↗
arXiv2019

Dimension constraints improve hypothesis testing for large-scale, graph-associated, brain-image data

For large-scale testing with graph-associated data, we present an empirical Bayes mixture technique to score local false discovery rates. Compared to empirical Bayes procedures that ignore the graph, the proposed method gains power in settings where non-null cases form connected subgraphs, and it does so by regularizing parameter contrasts between testing units. Simulations show that GraphMM controls the false discovery rate in a variety of settings. On magnetic resonance imaging data from a study of brain changes associated with the onset of Alzheimer's disease, GraphMM produces substantially greater yield than conventional large-scale testing procedures.

stat.ME↗
arXiv2015

Making the cut: improved ranking and selection for large-scale inference

Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to overpopulate lists of leading units with those associated with low measurement error. By contrast, local maximum likelihood (ML) approaches tend to favor units with high measurement error. Available Bayesian and empirical Bayesian approaches rely on specialized loss functions that result in similar deficiencies. We describe and evaluate a generic empirical Bayesian ranking procedure that populates the list of top units in a way that maximizes the expected overlap between the true and reported top lists for all list sizes. The procedure relates unit-specific posterior upper tail probabilities with their empirical distribution to yield a ranking variable. It discounts high-variance units less than popular non-ML methods and thus achieves improved operating characteristics in the models considered.

stat.ME↗
arXiv2015

A multi-functional analyzer uses parameter constraints to improve the efficiency of model-based gene-set analysis

We develop a model-based methodology for integrating gene-set information with an experimentally-derived gene list. The methodology uses a previously reported sampling model, but takes advantage of natural constraints in the high-dimensional discrete parameter space in order to work from a more structured prior distribution than is currently available. We show how the natural constraints are expressed in terms of linear inequality constraints within a set of binary latent variables. Further, the currently available prior gives low probability to these constraints in complex systems, such as Gene Ontology (GO), thus reducing the efficiency of statistical inference. We develop two computational advances to enable posterior inference within the constrained parameter space: one using integer linear programming for optimization and one using a penalized Markov chain sampler. Numerical experiments demonstrate the utility of the new methodology for a multivariate integration of genomic data with GO or related information systems. Compared to available methods, the proposed multi-functional analyzer covers more reported genes without mis-covering nonreported genes, as demonstrated on genome-wide data from association studies of type 2 diabetes and from RNA interference studies of influenza.

stat.ME↗
arXiv2012

Gamma-based clustering via ordered means with application to gene-expression analysis

Discrete mixture models provide a well-known basis for effective clustering algorithms, although technical challenges have limited their scope. In the context of gene-expression data analysis, a model is presented that mixes over a finite catalog of structures, each one representing equality and inequality constraints among latent expected values. Computations depend on the probability that independent gamma-distributed variables attain each of their possible orderings. Each ordering event is equivalent to an event in independent negative-binomial random variables, and this finding guides a dynamic-programming calculation. The structuring of mixture-model components according to constraints among latent means leads to strict concavity of the mixture log likelihood. In addition to its beneficial numerical properties, the clustering method shows promising results in an empirical study.

stat.ME↗
arXiv2007

Random-set methods identify distinct aspects of the enrichment signal in gene-set analysis

A prespecified set of genes may be enriched, to varying degrees, for genes that have altered expression levels relative to two or more states of a cell. Knowing the enrichment of gene sets defined by functional categories, such as gene ontology (GO) annotations, is valuable for analyzing the biological signals in microarray expression data. A common approach to measuring enrichment is by cross-classifying genes according to membership in a functional category and membership on a selected list of significantly altered genes. A small Fisher's exact test $p$-value, for example, in this $2\times2$ table is indicative of enrichment. Other category analysis methods retain the quantitative gene-level scores and measure significance by referring a category-level statistic to a permutation distribution associated with the original differential expression problem. We describe a class of random-set scoring methods that measure distinct components of the enrichment signal. The class includes Fisher's test based on selected genes and also tests that average gene-level evidence across the category. Averaging and selection methods are compared empirically using Affymetrix data on expression in nasopharyngeal cancer tissue, and theoretically using a location model of differential expression. We find that each method has a domain of superiority in the state space of enrichment problems, and that both methods have benefits in practice. Our analysis also addresses two problems related to multiple-category inference, namely, that equally enriched categories are not detected with equal probability if they are of different sizes, and also that there is dependence among category statistics owing to shared genes. Random-set enrichment calculations do not require Monte Carlo for implementation. They are made available in the R package allez.

stat.AP↗