Learning of low dimensional structure in multidimensional data is a canonical problem in machine learning. One common approach is to suppose that the observed data are close to a lower-dimensional smooth manifold. There are a rich variety of manifold learning methods available, which allow mapping of data points to the manifold. However, there is a clear lack of probabilistic methods that allow learning of the manifold along with the generative distribution of the observed data. The best attempt is the Gaussian process latent variable model (GP-L VM), but identifiability issues lead to poor performance. We solve these issues by proposing a novel Coulomb repulsive process (Corp) for locations of points on the manifold, inspired by physical models of electrostatic interactions among particles. Combining this process with a GP prior for the mapping function yields a novel electrostatic GP (electroGP) process. Focusing on the simple case of a one-dimensional manifold, we develop efficient inference algorithms, and illustrate substantially improved performance in a variety of experiments including filling in missing frames in video.

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

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

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

Instead of considering "online" and "continual" learning as inconvenient constraints to avoid, in

We extend the theory of boosting for regression problems to the online learning setting. Generalizing from the batch setting for boosting, the notion of a weak learning algorithm is modeled as an online learning algorithm with linear loss functions that competes with a base class of regression functions, while a strong learning algorithm is an online learning algorithm with smooth convex loss functions that competes with a larger class of regression functions. Our main result is an online gradient boosting algorithm that converts a weak online learning algorithm into a strong one where the larger class of functions is the linear span of the base class. We also give a simpler boosting algorithm that converts a weak online learning algorithm into a strong one where the larger class of functions is the convex hull of the base class, and prove its optimality.

We study the problem of sequentially testing individuals for a binary disease outcome whose true risk is governed by an unknown logistic model. At each round, a patient arrives with feature vector $x_t$, and the decision maker may either pay to administer a (noiseless) diagnostic test--revealing the true label--or skip testing and predict the patient's disease status based on their feature vector and prior history. Our goal is to minimize the total number of costly tests required while guaranteeing that the fraction of misclassifications does not exceed a prespecified error tolerance $α$, with probability at least $1-δ$. To address this, we develop a novel algorithm that interleaves label-collection and distribution estimation to estimate both $θ^{*}$ and the context distribution $P$, and computes a conservative, data-driven threshold $τ_t$ on the logistic score $|x_t^\topθ|$ to decide when testing is necessary. We prove that, with probability at least $1-δ$, our procedure does not exceed the target misclassification rate, and requires only $O(\sqrt{T})$ excess tests compared to the oracle baseline that knows both $θ^{*}$ and the patient feature distribution $P$. This establishes the first no-regret guarantees for error-constrained logistic testing, with direct applications to cost-sensitive medical screening. Simulations corroborate our theoretical guarantees, showing that in practice our procedure efficiently estimates $θ^{*}$ while retaining safety guarantees, and does not require too many excess tests.

Simultaneously performing variable selection and inference in high-dimensional models is an open challenge in statistics and machine learning. The increasing availability of vast amounts of variables requires the adoption of specific statistical procedures to accurately select the most important predictors in a high-dimensional space, while being able to control some form of selection error. In this work we adapt the Mirror Statistic approach to False Discovery Rate (FDR) control into a Bayesian modelling framework. The Mirror Statistic, developed in the classic frequentist statistical framework, is a flexible method to control FDR, which only requires mild model assumptions, but requires two sets of independent regression coefficient estimates, usually obtained after splitting the original dataset. Here we propose to rely on a Bayesian formulation of the model and use the posterior distributions of the coefficients of interest to build the Mirror Statistic and effectively control the FDR without the need to split the data. Moreover, the method is very flexible since it can be used with continuous and discrete outcomes and more complex predictors, such as with mixed models. We keep the approach scalable to high-dimensions by relying on Automatic Differentiation Variational Inference and fully continuous prior choices.