Although the recent progress is substantial, deep learning methods can be vulnerable to the maliciously generated adversarial examples.

Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning.

We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-sized vector indicating the membership to metastable (long-lived) states, (ii) a Markov chain that governs the transitions between metastable states and facilitates analysis of the long-time dynamics, and (iii) a generative part that samples the conditional distribution of configurations in the next time step. The model can be operated in a recursive fashion to generate trajectories to predict the system evolution from a defined starting state and propose new configurations. The DeepGenMSM is demonstrated to provide accurate estimates of the long-time kinetics and generate valid distributions for molecular dynamics (MD) benchmark systems. Remarkably, we show that DeepGenMSMs are able to make long time-steps in molecular configuration space and generate physically realistic structures in regions that were not seen in training data.

V ariational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence.

Active learning is the task of using labelled data to select additional points to label, with the goal of fitting the most accurate model with a fixed budget of labelled points. In binary classification active learning is known to produce faster rates than passive learning for a broad range of settings. However in regression restrictive structure and tailored methods were previously needed to obtain theoretically superior performance. In this paper we propose an intuitive tree based active learning algorithm for non-parametric regression with provable improvement over random sampling. When implemented with Mondrian Trees our algorithm is tuning parameter free, consistent and minimax optimal for Lipschitz functions.

In this paper, we focus on the problem of community detection for a simple two-class Stochastic Blockmodel (SBM).

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties.

This paper proposes a stochastic variant of a classic algorithm--the cubic-regularized Newton method [Nesterov and Polyak, 2006].

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

Even for applications with nonconvex nonsmooth losses (such as modern deep networks), the population risk is generally significantly more well-behaved from an optimization point of view than the empirical risk.