More Like this

1. GRASP: a goodness-of-fit test for classification learning

   https://doi.org/10.1093/jrsssb/qkad106  

   Javanmard, Adel; Mehrabi, Mohammad (September 2023, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Abstract Performance of classifiers is often measured in terms of average accuracy on test data. Despite being a standard measure, average accuracy fails in characterising the fit of the model to the underlying conditional law of labels given the features vector (Y∣X), e.g. due to model misspecification, over fitting, and high-dimensionality. In this paper, we consider the fundamental problem of assessing the goodness-of-fit for a general binary classifier. Our framework does not make any parametric assumption on the conditional law Y∣X and treats that as a black-box oracle model which can be accessed only through queries. We formulate the goodness-of-fit assessment problem as a tolerance hypothesis testing of the form H0:E[Df(Bern(η(X))‖Bern(η^(X)))]≤τ where Df represents an f-divergence function, and η(x), η^(x), respectively, denote the true and an estimate likelihood for a feature vector x admitting a positive label. We propose a novel test, called Goodness-of-fit with Randomisation and Scoring Procedure (GRASP) for testing H0, which works in finite sample settings, no matter the features (distribution-free). We also propose model-X GRASP designed for model-X settings where the joint distribution of the features vector is known. Model-X GRASP uses this distributional information to achieve better power. We evaluate the performance of our tests through extensive numerical experiments. 

   more » « less
2. Learning cycle-consistent cooperative networks via alternating MCMC teaching for unsupervised cross-domain translation

   Xie, J; Zheng, Z; Fang, X; Zhu, S C; Wu, Y N (January 2021, Proceedings of the AAAI Conference on Artificial Intelligence)

   This paper studies the unsupervised cross-domain translation problem by proposing a generative framework, in which the probability distribution of each domain is represented by a generative cooperative network that consists of an energy based model and a latent variable model. The use of generative cooperative network enables maximum likelihood learning of the domain model by MCMC teaching, where the energy-based model seeks to fit the data distribution of domain and distills its knowledge to the latent variable model via MCMC. Specifically, in the MCMC teaching process, the latent variable model parameterized by an encoder-decoder maps examples from the source domain to the target domain, while the energy-based model further refines the mapped results by Langevin revision such that the revised results match to the examples in the target domain in terms of the statistical properties, which are defined by the learned energy function. For the purpose of building up a correspondence between two unpaired domains, the proposed framework simultaneously learns a pair of cooperative networks with cycle consistency, accounting for a two-way translation between two domains, by alternating MCMC teaching. Experiments show that the proposed framework is useful for unsupervised image-to-image translation and unpaired image sequence translation. 

   more » « less
3. Simulation-Based Inference with Approximately Correct Parameters via Maximum Entropy

   Barrett, Rainier; Ansari, Mehrad; Ghosal, Gourab; White, Andrew D (April 2021, ArXivorg)

   null (Ed.)

   Inferring the input parameters of simulators from observations is a crucial challenge with applications from epidemiology to molecular dynamics. Here we show a simple approach in the regime of sparse data and approximately correct models, which is common when trying to use an existing model to infer latent variables with observed data. This approach is based on the principle of maximum entropy (MaxEnt) and provably makes the smallest change in the latent joint distribution to fit new data. This method requires no likelihood or model derivatives and its fit is insensitive to prior strength, removing the need to balance observed data fit with prior belief. The method requires the ansatz that data is fit in expectation, which is true in some settings and may be reasonable in all with few data points. The method is based on sample reweighting, so its asymptotic run time is independent of prior distribution dimension. We demonstrate this MaxEnt approach and compare with other likelihood-free inference methods across three systems: a point particle moving in a gravitational field, a compartmental model of epidemic spread and finally molecular dynamics simulation of a protein. 

   more » « less
4. Complexity of High-Dimensional Identity Testing with Coordinate Conditional Sampling

   Blanca, Antonio; Chen, Zongchen; Štefankovič, Daniel; Vigoda, Eric (August 2023, COLT 2023)

   We study the identity testing problem for high-dimensional distributions. Given as input an explicit distribution μ, an ε>0, and access to sampling oracle(s) for a hidden distribution π, the goal in identity testing is to distinguish whether the two distributions μ and π are identical or are at least ε-far apart. When there is only access to full samples from the hidden distribution π, it is known that exponentially many samples (in the dimension) may be needed for identity testing, and hence previous works have studied identity testing with additional access to various “conditional” sampling oracles. We consider a significantly weaker conditional sampling oracle, which we call the Coordinate Oracle, and provide a computational and statistical characterization of the identity testing problem in this new model. We prove that if an analytic property known as approximate tensorization of entropy holds for an n-dimensional visible distribution μ, then there is an efficient identity testing algorithm for any hidden distribution π using O˜(n/ε) queries to the Coordinate Oracle. Approximate tensorization of entropy is a pertinent condition as recent works have established it for a large class of high-dimensional distributions. We also prove a computational phase transition: for a well-studied class of n-dimensional distributions, specifically sparse antiferromagnetic Ising models over {+1,−1}^n, we show that in the regime where approximate tensorization of entropy fails, there is no efficient identity testing algorithm unless RP=NP. We complement our results with a matching Ω(n/ε) statistical lower bound for the sample complexity of identity testing in the model. 

   more » « less
5. Ensemble estimation and variable selection with semiparametric regression models

   https://doi.org/10.1093/biomet/asaa012  

   Shin, Sunyoung; Liu, Yufeng; Cole, Stephen R; Fine, Jason P (April 2020, Biometrika)

   Summary We consider scenarios in which the likelihood function for a semiparametric regression model factors into separate components, with an efficient estimator of the regression parameter available for each component. An optimal weighted combination of the component estimators, named an ensemble estimator, may be employed as an overall estimate of the regression parameter, and may be fully efficient under uncorrelatedness conditions. This approach is useful when the full likelihood function may be difficult to maximize, but the components are easy to maximize. It covers settings where the nuisance parameter may be estimated at different rates in the component likelihoods. As a motivating example we consider proportional hazards regression with prospective doubly censored data, in which the likelihood factors into a current status data likelihood and a left-truncated right-censored data likelihood. Variable selection is important in such regression modelling, but the applicability of existing techniques is unclear in the ensemble approach. We propose ensemble variable selection using the least squares approximation technique on the unpenalized ensemble estimator, followed by ensemble re-estimation under the selected model. The resulting estimator has the oracle property such that the set of nonzero parameters is successfully recovered and the semiparametric efficiency bound is achieved for this parameter set. Simulations show that the proposed method performs well relative to alternative approaches. Analysis of an AIDS cohort study illustrates the practical utility of the method. 

   more » « less