Guaranteed Non-Asymptotic Confidence Ellipsoids for FIR Systems

Recently, a new finite-sample system identification algorithm, called Sign-Perturbed Sums (SPS), was introduced in [2]. SPS constructs finite-sample confidence regions that are centered around the least squares estimate, and are guaranteed to contain the true system parameters with a user-chosen exact probability for any finite number of data points. The main assumption of SPS is that the noise terms are independent and symmetrically distributed about zero, but they do not have to be stationary, nor do their variances and distributions have to be known. Although it is easy to determine if a particular parameter belongs to the confidence region, it is not easy to describe the boundary of the region, and hence to compactly represent the exact confidence region. In this paper we show that an ellipsoidal outer-approximation of the SPS confidence region can be found by solving a convex optimization problem, and we illustrate the properties of the SPS region and the ellipsoidal outer-approximation in simulation examples

Adaptive Aggregated Predictions for Renewable Energy Systems

The paper addresses the problem of generating forecasts for energy production and consumption processes in a renewable energy system. The forecasts are made for a prototype public lighting microgrid, which includes photovoltaic panels and LED luminaries that regulate their lighting levels, as inputs for a receding horizon controller. Several stochastic models are fitted to historical times-series data and it is argued that side information, such as clear-sky predictions or the typical system behavior, can be used as exogenous inputs to increase their performance. The predictions can be further improved by combining the forecasts of several models using online learning, the framework of prediction with expert advice. The paper suggests an adaptive aggregation method which also takes side information into account, and makes a state-dependent aggregation. Numerical experiments are presented, as well, showing the efficiency of the estimated timeseries models and the proposed aggregation approach

Online Learning for Aggregating Forecasts in Renewable Energy Systems

One of the key problems in renewable energy systems is how to model and forecast the energy flow. The paper first investigates various stochastic times-series models to predict energy production and consumption, then suggests an online learning method which adaptively aggregates the different forecasts while also taking side information into account. The approach is demonstrated on data coming from a prototype public lighting microgrid which includes photovoltaic panels and LED luminaries

Efficient Clothing Fitting from Data.

A major drawback of shopping for clothes on-line is that the customer cannot try on clothes and see if they fit or suit them. One solution is to display clothing on an avatar, a 3D graphical model of the customer. However the normal technique for modeling clothing in computer graphics, cloth dynamics, suffers from being too processor intensive and is not practical for real time applications. Hence, retailers normally rely on a fixed set of body models to which clothes are pre-fitted. As the customer has to choose from this limited set the fit is typicallly not very representative of how the real clothes will fit. We propose a method that uses a compromise between these two methods. We generate a set of example avatars by performing Principal Component Analysis on a dataset of avatars. Clothes are pre-fitted to these examples off-line. Instead of asking the customer to choose from the set of examples we are able to represent the users avatar as a weighted sum of the examples, we then fit clothes as the same weighted sum over the clothes fitted to the examples

Distribution-Free Uncertainty Quantification for Kernel Methods by Gradient Perturbations

We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or exponential families, it only requires knowledge about some mild regularity of the measurement noise, such as it is being symmetric or exchangeable. We show, by building on recent results from finite-sample system identification, that by perturbing the residuals in the gradient of the objective function, information can be extracted about the amount of uncertainty our model has. Particularly, we provide an algorithm to build exact, non-asymptotically guaranteed, distribution-free confidence regions for ideal, noise-free representations of the function we try to estimate. For the typical convex quadratic problems and symmetric noises, the regions are star convex centered around a given nominal estimate, and have efficient ellipsoidal outer approximations. Finally, we illustrate the ideas on typical kernel methods, such as LS-SVC, KRR, $\varepsilon$-SVR and kernelized LASSO.Comment: 18 figure