arXiv subjects

Alejandro Catalina

Publications and source records attributed to Alejandro Catalina.

5 recordsLinked to original sources

arXiv2021

Latent space projection predictive inference

Given a reference model that includes all the available variables, projection predictive inference replaces its posterior with a constrained projection including only a subset of all variables. We extend projection predictive inference to enable computationally efficient variable and structure selection in models outside the exponential family. By adopting a latent space projection predictive perspective we are able to: 1) propose a unified and general framework to do variable selection in complex models while fully honouring the original model structure, 2) properly identify relevant structure and retain posterior uncertainties from the original model, and 3) provide an improved approach also for non-Gaussian models in the exponential family. We demonstrate the superior performance of our approach by thoroughly testing and comparing it against popular variable selection approaches in a wide range of settings, including realistic data sets. Our results show that our approach successfully recovers relevant terms and model structure in complex models, selecting less variables than competing approaches for realistic datasets.

stat.CO↗

arXiv2021

Challenges and Opportunities in High-dimensional Variational Inference

Current black-box variational inference (BBVI) methods require the user to make numerous design choices -- such as the selection of variational objective and approximating family -- yet there is little principled guidance on how to do so. We develop a conceptual framework and set of experimental tools to understand the effects of these choices, which we leverage to propose best practices for maximizing posterior approximation accuracy. Our approach is based on studying the pre-asymptotic tail behavior of the density ratios between the joint distribution and the variational approximation, then exploiting insights and tools from the importance sampling literature. Our framework and supporting experiments help to distinguish between the behavior of BBVI methods for approximating low-dimensional versus moderate-to-high-dimensional posteriors. In the latter case, we show that mass-covering variational objectives are difficult to optimize and do not improve accuracy, but flexible variational families can improve accuracy and the effectiveness of importance sampling -- at the cost of additional optimization challenges. Therefore, for moderate-to-high-dimensional posteriors we recommend using the (mode-seeking) exclusive KL divergence since it is the easiest to optimize, and improving the variational family or using model parameter transformations to make the posterior and optimal variational approximation more similar. On the other hand, in low-dimensional settings, we show that heavy-tailed variational families and mass-covering divergences are effective and can increase the chances that the approximation can be improved by importance sampling.

cs.LG↗

arXiv2020

Projection Predictive Inference for Generalized Linear and Additive Multilevel Models

Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive inference projects its posterior onto a constrained space of a subset of variables. Variable selection is then performed by sequentially adding relevant variables until predictive performance is satisfactory. Previously, projection predictive inference has been demonstrated only for generalized linear models (GLMs) and Gaussian processes (GPs) where it showed superior performance to competing variable selection procedures. In this work, we extend projection predictive inference to support variable and structure selection for generalized linear multilevel models (GLMMs) and generalized additive multilevel models (GAMMs). Our simulative and real-word experiments demonstrate that our method can drastically reduce the model complexity required to reach reference predictive performance and achieve good frequency properties.

stat.ME↗

arXiv2020

Robust, Accurate Stochastic Optimization for Variational Inference

We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior distribution,(2) the choice of divergence, and (3) the optimization of the variational objective. We show that even in the best-case scenario when the exact posterior belongs to the assumed variational family, common stochastic optimization methods lead to poor variational approximations if the problem dimension is moderately large. We also demonstrate that these methods are not robust across diverse model types. Motivated by these findings, we develop a more robust and accurate stochastic optimization framework by viewing the underlying optimization algorithm as producing a Markov chain. Our approach is theoretically motivated and includes a diagnostic for convergence and a novel stopping rule, both of which are robust to noisy evaluations of the objective function. We show empirically that the proposed framework works well on a diverse set of models: it can automatically detect stochastic optimization failure or inaccurate variational approximation

cs.LG↗

arXiv2020

Group Heterogeneity Assessment for Multilevel Models

Many data sets contain an inherent multilevel structure, for example, because of repeated measurements of the same observational units. Taking this structure into account is critical for the accuracy and calibration of any statistical analysis performed on such data. However, the large number of possible model configurations hinders the use of multilevel models in practice. In this work, we propose a flexible framework for efficiently assessing differences between the levels of given grouping variables in the data. The assessed group heterogeneity is valuable in choosing the relevant group coefficients to consider in a multilevel model. Our empirical evaluations demonstrate that the framework can reliably identify relevant multilevel components in both simulated and real data sets.

stat.ME↗