Probabilistic Methods 3

Moderator: Guillaume Bouchard


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Thu 22 July 7:00 - 7:20 PDT

DG-LMC: A Turn-key and Scalable Synchronous Distributed MCMC Algorithm via Langevin Monte Carlo within Gibbs

Vincent Plassier · Maxime Vono · Alain Durmus · Eric Moulines

Performing reliable Bayesian inference on a big data scale is becoming a keystone in the modern era of machine learning. A workhorse class of methods to achieve this task are Markov chain Monte Carlo (MCMC) algorithms and their design to handle distributed datasets has been the subject of many works. However, existing methods are not completely either reliable or computationally efficient. In this paper, we propose to fill this gap in the case where the dataset is partitioned and stored on computing nodes within a cluster under a master/slaves architecture. We derive a user-friendly centralised distributed MCMC algorithm with provable scaling in high-dimensional settings. We illustrate the relevance of the proposed methodology on both synthetic and real data experiments.

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Thu 22 July 7:20 - 7:25 PDT

Nonmyopic Multifidelity Acitve Search

Quan Nguyen · Arghavan Modiri · Roman Garnett

Active search is a learning paradigm where we seek to identify as many members of a rare, valuable class as possible given a labeling budget. Previous work on active search has assumed access to a faithful (and expensive) oracle reporting experimental results. However, some settings offer access to cheaper surrogates such as computational simulation that may aid in the search. We propose a model of multifidelity active search, as well as a novel, computationally efficient policy for this setting that is motivated by state-of-the-art classical policies. Our policy is nonmyopic and budget aware, allowing for a dynamic tradeoff between exploration and exploitation. We evaluate the performance of our solution on real-world datasets and demonstrate significantly better performance than natural benchmarks.

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Thu 22 July 7:25 - 7:30 PDT

Active Testing: Sample-Efficient Model Evaluation

Jannik Kossen · Sebastian Farquhar · Yarin Gal · Tom Rainforth

We introduce a new framework for sample-efficient model evaluation that we call active testing. While approaches like active learning reduce the number of labels needed for model training, existing literature largely ignores the cost of labeling test data, typically unrealistically assuming large test sets for model evaluation. This creates a disconnect to real applications, where test labels are important and just as expensive, e.g. for optimizing hyperparameters. Active testing addresses this by carefully selecting the test points to label, ensuring model evaluation is sample-efficient. To this end, we derive theoretically-grounded and intuitive acquisition strategies that are specifically tailored to the goals of active testing, noting these are distinct to those of active learning. As actively selecting labels introduces a bias; we further show how to remove this bias while reducing the variance of the estimator at the same time. Active testing is easy to implement and can be applied to any supervised machine learning method. We demonstrate its effectiveness on models including WideResNets and Gaussian processes on datasets including Fashion-MNIST and CIFAR-100.

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Thu 22 July 7:30 - 7:35 PDT

Oblivious Sketching for Logistic Regression

Alexander Munteanu · Simon Omlor · David Woodruff

What guarantees are possible for solving logistic regression in one pass over a data stream? To answer this question, we present the first data oblivious sketch for logistic regression. Our sketch can be computed in input sparsity time over a turnstile data stream and reduces the size of a $d$-dimensional data set from $n$ to only $\operatorname{poly}(\mu d\log n)$ weighted points, where $\mu$ is a useful parameter which captures the complexity of compressing the data. Solving (weighted) logistic regression on the sketch gives an $O(\log n)$-approximation to the original problem on the full data set. We also show how to obtain an $O(1)$-approximation with slight modifications. Our sketches are fast, simple, easy to implement, and our experiments demonstrate their practicality.

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Thu 22 July 7:35 - 7:40 PDT

SGLB: Stochastic Gradient Langevin Boosting

Aleksei Ustimenko · Liudmila Prokhorenkova

This paper introduces Stochastic Gradient Langevin Boosting (SGLB) - a powerful and efficient machine learning framework that may deal with a wide range of loss functions and has provable generalization guarantees. The method is based on a special form of the Langevin diffusion equation specifically designed for gradient boosting. This allows us to theoretically guarantee the global convergence even for multimodal loss functions, while standard gradient boosting algorithms can guarantee only local optimum. We also empirically show that SGLB outperforms classic gradient boosting when applied to classification tasks with 0-1 loss function, which is known to be multimodal.

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Thu 22 July 7:40 - 7:45 PDT

Flow-based Attribution in Graphical Models: A Recursive Shapley Approach

Raghav Singal · George Michailidis · Hoiyi Ng

We study the attribution problem in a graphical model, wherein the objective is to quantify how the effect of changes at the source nodes propagates through the graph. We develop a model-agnostic flow-based attribution method, called recursive Shapley value (RSV). RSV generalizes a number of existing node-based methods and uniquely satisfies a set of flow-based axioms. In addition to admitting a natural characterization for linear models and facilitating mediation analysis for non-linear models, RSV satisfies a mix of desirable properties discussed in the recent literature, including implementation invariance, sensitivity, monotonicity, and affine scale invariance.

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Thu 22 July 7:45 - 7:50 PDT

On the difficulty of unbiased alpha divergence minimization

Tomas Geffner · Justin Domke

Several approximate inference algorithms have been proposed to minimize an alpha-divergence between an approximating distribution and a target distribution. Many of these algorithms introduce bias, the magnitude of which becomes problematic in high dimensions. Other algorithms are unbiased. These often seem to suffer from high variance, but little is rigorously known. In this work we study unbiased methods for alpha-divergence minimization through the Signal-to-Noise Ratio (SNR) of the gradient estimator. We study several representative scenarios where strong analytical results are possible, such as fully-factorized or Gaussian distributions. We find that when alpha is not zero, the SNR worsens exponentially in the dimensionality of the problem. This casts doubt on the practicality of these methods. We empirically confirm these theoretical results.

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Thu 22 July 7:50 - 7:55 PDT