HE FORECASTING of power demand is of crucial importance for the development of modern power systems. The stable and efficient management, scheduling and dispatch in power systems rely heavily on precise forecasting of future loads on various time horizons. In particular, shortterm load forecasting (STLF) focuses on the forecasting of loads from several minutes up to one week into the future [1]. A reliable STLF helps utilities and energy providers deal with the challenges posed by the higher penetration of renewable energies and the development of electricity markets with increasingly complex pricing strategies in future smart grids. Various STLF methods have been proposed by researchers over the years. Some of the models used for STLF include linear or nonparametric regression [2], [3], support vector regression (SVR) [1], [4], autoregressive models [5], fuzzylogic approach [6], etc. Reviews and evaluations of existing methods can be found in [7]-[10]. Building STLF systems with artificial neural networks (ANN) has long been one of the mainstream solutions to this task. As early as 2001, a review paper by Hippert et al. surveyed and examined a collection of papers that had been published between 1991 and 1999, and arrived at the conclusions that most of the proposed models

Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration" phenomenon induced by random matrix theory to perform a spectral analysis on the Gram matrix of these random feature maps, here for Gaussian mixture models of simultaneously large dimension and size. Our results are instrumental to a deeper understanding on the interplay of the nonlinearity and the statistics of the data, thereby allowing for a better tuning of random feature-based techniques.

Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version that is less accurate but easy to differentiate. In this work we characterize the differential properties of the original Sinkhorn distance, proving that it enjoys the same smoothness as its regularized version and we explicitly provide an efficient algorithm to compute its gradient. We show that this result benefits both theory and applications: on one hand, high order smoothness confers statistical guarantees to learning with Wasserstein approximations. On the other hand, the gradient formula allows us to efficiently solve learning and optimization problems in practice. Promising preliminary experiments complement our analysis.

This paper presents a new class of gradient methods for distributed machine learning that adaptively skip the gradient calculations to learn with reduced communication and computation. Simple rules are designed to detect slowly-varying gradients and, therefore, trigger the reuse of outdated gradients. The resultant gradient-based algorithms are termed Lazily Aggregated Gradient --- justifying our acronym LAG used henceforth. Theoretically, the merits of this contribution are: i) the convergence rate is the same as batch gradient descent in strongly-convex, convex, and nonconvex smooth cases; and, ii) if the distributed datasets are heterogeneous (quantified by certain measurable constants), the communication rounds needed to achieve a targeted accuracy are reduced thanks to the adaptive reuse of lagged gradients. Numerical experiments on both synthetic and real data corroborate a significant communication reduction compared to alternatives.

Human lives are important. The decision to allow self-driving vehicles operate on our roads carries great weight. This has been a hot topic of debate between policy-makers, technologists and public safety institutions. The recent Uber Inc. self-driving car crash, resulting in the death of a pedestrian, has strengthened the argument that autonomous vehicle technology is still not ready for deployment on public roads. In this work, we analyze the Uber car crash and shed light on the question, "Could the Uber Car Crash have been avoided?". We apply state-of-the-art Computer Vision models to this highly practical scenario. More generally, our experimental results are an evaluation of various image enhancement and object recognition techniques for enabling pedestrian safety in low-lighting conditions using the Uber crash as a case study.

We propose a new way of deriving policy gradient updates for reinforcement learning. Our technique, based on Fourier analysis, recasts integrals that arise with expected policy gradients as convolutions and turns them into multiplications. The obtained analytical solutions allow us to capture the low variance benefits of EPG in a broad range of settings. For the critic, we treat trigonometric and radial basis functions, two function families with the universal approximation property. The choice of policy can be almost arbitrary, including mixtures or hybrid continuous-discrete probability distributions. Moreover, we derive a general family of sample-based estimators for stochastic policy gradients, which unifies existing results on sample-based approximation. We believe that this technique has the potential to shape the next generation of policy gradient approaches, powered by analytical results.

R language is a free statistical computing environment; hence there are multiple ways/packages to achieve a particular statistical/quantitative output. I am going to discuss here a concise list of R packages that one can use for the modeling of financial risks and/or portfolio optimization with utmost efficiency and effectiveness. The intended audience for this article is financial market analysts interested in using R, and also for quantitatively inclined folks with a background in finance, statistics, and mathematics. Given the rise in the frequency of crises (the frequency of occurrence of financial market crises has certainly increased during the last 18 years or so; since the 1999 bubble burst), the modeling and measurement of financial market risk have gained tremendously in importance and the focus of portfolio allocation has shifted from the average side of the (mean, SD) coin to the SD side. Hence, it has become necessary to devise and employ methods and techniques that are better able to cope with the empirically observed extreme fluctuations in the financial markets.

Logistic regression predicts the probability of the outcome being true. In this exercise, we will implement a logistic regression and apply it to two different data sets. To learn the basics of Logistic Regression in R read this post. In the first part of this exercise, we will build a logistic regression model to predict whether a student gets admitted into a university. Suppose that you are the administrator of a university department and you want to determine each applicant's chance of admission based on their results on two exams.

Logistic regression is the most famous machine learning algorithm after linear regression. In a lot of ways, linear regression and logistic regression are similar. But, the biggest difference lies in what they are used for. Linear regression algorithms are used to predict/forecast values but logistic regression is used for classification tasks. If you are shaky on the concepts of linear regression, check this out.

We develop a new learning-based approach to ill-posed inverse problems. Instead of directly learning the complex mapping from the measured data to the reconstruction, we learn an ensemble of simpler mappings from data to projections of the unknown model into random low-dimensional subspaces. We form the reconstruction by combining the estimated subspace projections. Structured subspaces of piecewise-constant images on random Delaunay triangulations allow us to address inverse problems with extremely sparse data and still get good reconstructions of the unknown geometry. This choice also makes our method robust against arbitrary data corruptions not seen during training. Further, it marginalizes the role of the training dataset which is essential for applications in geophysics where ground-truth datasets are exceptionally scarce.