Neural Information Processing Systems http://nips.cc/

A predictor that is deployed in a live production system may perturb the features it uses to make predictions. Such a feedback loop can occur, for example, when a model that predicts a certain type of behavior ends up causing the behavior it predicts, thus creating a self-fulfilling prophecy. In this paper we analyze predictor feedback detection as a causal inference problem, and introduce a local randomization scheme that can be used to detect non-linear feedback in real-world problems. We conduct a pilot study for our proposed methodology using a predictive system currently deployed as a part of a search engine.

We propose a distributed Markov chain Monte Carlo (MCMC) inference algorithm for large scale Bayesian posterior simulation. We assume that the dataset is partitioned and stored across nodes of a cluster. Our procedure involves an independent MCMC posterior sampler at each node based on its local partition of the data. Moment statistics of the local posteriors are collected from each sampler and propagated across the cluster using expectation propagation message passing with low communication costs. The moment sharing scheme improves posterior estimation quality by enforcing agreement among the samplers. We demonstrate the speed and inference quality of our method with empirical studies on Bayesian logistic regression and sparse linear regression with a spike-and-slab prior.

We develop a framework for post model selection inference, via marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response y, conditional on the model being selected ("condition on selection" framework). This allows us to construct valid confidence intervals and hypothesis tests for regression coefficients that account for the selection procedure. In contrast to recent work in high-dimensional statistics, our results are exact (non-asymptotic) and require no eigenvalue-like assumptions on the design matrix X. Furthermore, the computational cost of marginal regression, constructing confidence intervals and hypothesis testing is negligible compared to the cost of linear regression, thus making our methods particularly suitable for extremely large datasets. Although we focus on marginal screening to illustrate the applicability of the condition on selection framework, this framework is much more broadly applicable. We show how to apply the proposed framework to several other selection procedures including orthogonal matching pursuit and marginal screening+Lasso.

In this paper, we address the problem of learning the structure of Gaussian chain graph models in a high-dimensional space. Chain graph models are generalizations of undirected and directed graphical models that contain a mixed set of directed and undirected edges. While the problem of sparse structure learning has been studied extensively for Gaussian graphical models and more recently for conditional Gaussian graphical models (CGGMs), there has been little previous work on the structure recovery of Gaussian chain graph models. We consider linear regression models and a re-parameterization of the linear regression models using CGGMs as building blocks of chain graph models. We argue that when the goal is to recover model structures, there are many advantages of using CGGMs as chain component models over linear regression models, including convexity of the optimization problem, computational efficiency, recovery of structured sparsity, and ability to leverage the model structure for semi-supervised learning. We demonstrate our approach on simulated and genomic datasets.

We study the residual bootstrap (RB) method in the context of high-dimensional linear regression.

We consider logistic regression with arbitrary outliers in the covariate matrix. We propose a new robust logistic regression algorithm, called RoLR, that estimates the parameter through a simple linear programming procedure. We prove that RoLR is robust to a constant fraction of adversarial outliers. To the best of our knowledge, this is the first result on estimating logistic regression model when the covariate matrix is corrupted with any performance guarantees. Besides regression, we apply RoLR to solving binary classification problems where a fraction of training samples are corrupted.

Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence that was developed for regression diagnostics can be used to detect such corrupted observations as shown in this paper. This property of influence - for which we also develop a randomized approximation - motivates our proposed subsampling algorithm for large scale corrupted linear regression which limits the influence of data points since highly influential points contribute most to the residual error. Under a general model of corrupted observations, we show theoretically and empirically on a variety of simulated and real datasets that our algorithm improves over the current state-of-the-art approximation schemes for ordinary least squares.

We propose a new active learning algorithm for parametric linear regression with random design. We provide finite sample convergence guarantees for general distributions in the misspecified model. This is the first active learner for this setting that provably can improve over passive learning. Unlike other learning settings (such as classification), in regression the passive learning rate of O(1/ɛ) cannot in general be improved upon. Nonetheless, the so-called'constant' in the rate of convergence, which is characterized by a distribution-dependent risk, can be improved in many cases. For a given distribution, achieving the optimal risk requires prior knowledge of the distribution. Following the stratification technique advocated in Monte-Carlo function integration, our active learner approaches the optimal risk using piecewise constant approximations.

We study the performance of empirical risk minimization on the p -norm linear regression problem for p \in (1, \infty) . We show that, in the realizable case, under no moment assumptions, and up to a distribution-dependent constant, O(d) samples are enough to exactly recover the target. Otherwise, for p \in [2, \infty), and under weak moment assumptions on the target and the covariates, we prove a high probability excess risk bound on the empirical risk minimizer whose leading term matches, up to a constant that depends only on p, the asymptotically exact rate. We extend this result to the case p \in (1, 2) under mild assumptions that guarantee the existence of the Hessian of the risk at its minimizer.