We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian inference method that generalizes Stein Variational Gradient Descent (SVGD) to Riemann manifold. The benefits are two-folds: (i) for inference tasks in Euclidean spaces, RSVGD has the advantage over SVGD of utilizing information geometry, and (ii) for inference tasks on Riemann manifolds, RSVGD brings the unique advantages of SVGD to the Riemannian world. To appropriately transfer to Riemann manifolds, we conceive novel and non-trivial techniques for RSVGD, which are required by the intrinsically different characteristics of general Riemann manifolds from Euclidean spaces. We also discover Riemannian Stein's Identity and Riemannian Kernelized Stein Discrepancy. Experimental results show the advantages over SVGD of exploring distribution geometry and the advantages of particle-efficiency, iteration-effectiveness and approximation flexibility over other inference methods on Riemann manifolds.

We introduce a framework using Generative Adversarial Networks (GANs) for likelihood--free inference (LFI) and Approximate Bayesian Computation (ABC). Our approach addresses both the key problems in likelihood--free inference, namely how to compare distributions and how to efficiently explore the parameter space. Our framework allows one to use the simulator model as a black box and leverage the power of deep networks to generate a rich set of features in a data driven fashion (as opposed to previous ad hoc approaches). Thereby it is a step towards a powerful alternative approach to LFI and ABC. On benchmark data sets, our approach improves on others with respect to scalability, ability to handle high dimensional data and complex probability distributions.

Rainfall ensemble forecasts have to be skillful for both low precipitation and extreme events. We present statistical post-processing methods based on Quantile Regression Forests (QRF) and Gradient Forests (GF) with a parametric extension for heavy-tailed distributions. Our goal is to improve ensemble quality for all types of precipitation events, heavy-tailed included, subject to a good overall performance. Our hybrid proposed methods are applied to daily 51-h forecasts of 6-h accumulated precipitation from 2012 to 2015 over France using the M{\'e}t{\'e}o-France ensemble prediction system called PEARP. They provide calibrated pre-dictive distributions and compete favourably with state-of-the-art methods like Analogs method or Ensemble Model Output Statistics. In particular, hybrid forest-based procedures appear to bring an added value to the forecast of heavy rainfall.

Learning from many real-world datasets is limited by a problem called the class imbalance problem. A dataset is imbalanced when one class (the majority class) has significantly more samples than the other class (the minority class). Such datasets cause typical machine learning algorithms to perform poorly on the classification task. To overcome this issue, this paper proposes a new approach Neighbors Progressive Competition (NPC) for classification of imbalanced datasets. Whilst the proposed algorithm is inspired by weighted k-Nearest Neighbor (k-NN) algorithms, it has major differences from them. Unlike k- NN, NPC does not limit its decision criteria to a preset number of nearest neighbors. In contrast, NPC considers progressively more neighbors of the query sample in its decision making until the sum of grades for one class is much higher than the other classes. Furthermore, NPC uses a novel method for grading the training samples to compensate for the imbalance issue. The grades are calculated using both local and global information. In brief, the contribution of this paper is an entirely new classifier for handling the imbalance issue effectively without any manually-set parameters or any need for expert knowledge. Experimental results compare the proposed approach with five representative algorithms applied to fifteen imbalanced datasets and illustrate this algorithms effectiveness.

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has been increasingly popular in Bayesian learning due to its ability to deal with large data. A standard SG-MCMC algorithm simulates samples from a discretized-time Markov chain to approximate a target distribution. However, the samples are typically highly correlated due to the sequential generation process, an undesired property in SG-MCMC. In contrary, Stein variational gradient descent (SVGD) directly optimizes a set of particles, and it is able to approximate a target distribution with much fewer samples. In this paper, we propose a novel method to directly optimize particles (or samples) in SG-MCMC from scratch. Specifically, we propose efficient methods to solve the corresponding Fokker-Planck equation on the space of probability distributions, whose solution (i.e., a distribution) is approximated by particles. Through our framework, we are able to show connections of SG-MCMC to SVGD, as well as the seemly unrelated generative-adversarial-net framework. Under certain relaxations, particle optimization in SG-MCMC can be interpreted as an extension of standard SVGD with momentum.

We consider the problem of semi-supervised few-shot classification (when the few labeled samples are accompanied with unlabeled data) and show how to adapt the Prototypical Networks [10] to this problem. We first show that using larger and better regularized prototypical networks can improve the classification accuracy. We then show further improvements by making use of unlabeled data.

This paper studies directed exploration for reinforcement learning agents by tracking uncertainty about the value of each available action. We identify two sources of uncertainty that are relevant for exploration. The first originates from limited data (parametric uncertainty), while the second originates from the distribution of the returns (return uncertainty). We identify methods to learn these distributions with deep neural networks, where we estimate parametric uncertainty with Bayesian drop-out, while return uncertainty is propagated through the Bellman equation as a Gaussian distribution. Then, we identify that both can be jointly estimated in one network, which we call the Double Uncertain Value Network. The policy is directly derived from the learned distributions based on Thompson sampling. Experimental results show that both types of uncertainty may vastly improve learning in domains with a strong exploration challenge.

Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to numerous other disciplines, including machine learning. Tensors and their decompositions are especially beneficial in unsupervised learning settings, but are gaining popularity in other sub-disciplines like temporal and multi-relational data analysis, too. The scope of this paper is to give a broad overview of tensors, their decompositions, and how they are used in machine learning. As part of this, we are going to introduce basic tensor concepts, discuss why tensors can be considered more rigid than matrices with respect to the uniqueness of their decomposition, explain the most important factorization algorithms and their properties, provide concrete examples of tensor decomposition applications in machine learning, conduct a case study on tensor-based estimation of mixture models, talk about the current state of research, and provide references to available software libraries.

Ordinary least square (OLS) estimation of a linear regression model is well-known to be highly sensitive to outliers. It is common practice to first identify and remove outliers by looking at the data then to fit OLS and form confidence intervals and p-values on the remaining data as if this were the original data collected. We show in this paper that this "detect-and-forget" approach can lead to invalid inference, and we propose a framework that properly accounts for outlier detection and removal to provide valid confidence intervals and hypothesis tests. Our inferential procedures apply to any outlier removal procedure that can be characterized by a set of quadratic constraints on the response vector, and we show that several of the most commonly used outlier detection procedures are of this form. Our methodology is built upon recent advances in selective inference (Taylor & Tibshirani 2015), which are focused on inference corrected for variable selection. We conduct simulations to corroborate the theoretical results, and we apply our method to two classic data sets considered in the outlier detection literature to illustrate how our inferential results can differ from the traditional detect-and-forget strategy. A companion R package, outference, implements these new procedures with an interface that matches the functions commonly used for inference with lm in R.

The segmentation of large scale power grids into zones allows a better understanding of its structure, as the control room operators will naturally but manually do for any study. In this paper we provide a new automatic hierarchical method based on the community detection algorithm \textit{Infomap}. Our main contribution is to offer as input a new representation of the power grid, called the security analysis, that represents power flow affinities beyond the connectivity of the grid, a point that will become even more relevant for tomorrow's cyber-physical system. Indeed we already discover few relevant and important clusters that are not connected in the actual grid topology. To better describe and investigate the method, we apply it here on the well-studied IEEE-RTS-96 and IEEE-118. We further applied our method on the large-scale French Power Grid which showed promising results given its puzzling resemblance with the historical RTE regional segmentation.