While it has not yet been proven, empirical evidence suggests that model generalization is related to local properties of the optima which can be described via the Hessian. We connect model generalization with the local property of a solution under the PAC-Bayes paradigm. In particular, we prove that model generalization ability is related to the Hessian, the higher-order "smoothness" terms characterized by the Lipschitz constant of the Hessian, and the scales of the parameters. Guided by the proof, we propose a metric to score the generalization capability of the model, as well as an algorithm that optimizes the perturbed model accordingly.

Water managers in the western United States (U.S.) rely on longterm forecasts of temperature and precipitation to prepare for droughts and other wet weather extremes. To improve the accuracy of these longterm forecasts, the Bureau of Reclamation and the National Oceanic and Atmospheric Administration (NOAA) launched the Subseasonal Climate Forecast Rodeo, a year-long real-time forecasting challenge, in which participants aimed to skillfully predict temperature and precipitation in the western U.S. two to four weeks and four to six weeks in advance. Here we present and evaluate our machine learning approach to the Rodeo and release our SubseasonalRodeo dataset, collected to train and evaluate our forecasting system. Our system is an ensemble of two regression models. The first integrates the diverse collection of meteorological measurements and dynamic model forecasts in the SubseasonalRodeo dataset and prunes irrelevant predictors using a customized multitask model selection procedure. The second uses only historical measurements of the target variable (temperature or precipitation) and introduces multitask nearest neighbor features into a weighted local linear regression. Each model alone is significantly more accurate than the operational U.S. Climate Forecasting System (CFSv2), and our ensemble skill exceeds that of the top Rodeo competitor for each target variable and forecast horizon. We hope that both our dataset and our methods will serve as valuable benchmarking tools for the subseasonal forecasting problem.

One of the main open problems of the theory of margin multi-category pattern classification is the characterization of the way the confidence interval of a guaranteed risk should vary as a function of the three basic parameters which are the sample size m, the number C of categories and the scale parameter gamma. This is especially the case when working under minimal learnability hypotheses. In that context, the derivation of a bound is based on the handling of capacity measures belonging to three main families: Rademacher/Gaussian complexities, metric entropies and scale-sensitive combinatorial dimensions. The scale-sensitive combinatorial dimensions dedicated to the classifiers of interest are the gamma-Psi-dimensions. This article introduces the combinatorial and structural results needed to involve them in the derivation of guaranteed risks. Such a bound is then established, under minimal hypotheses regarding the classifier. Its dependence on m, C and gamma is characterized. The special case of multi-class support vector machines is used to illustrate the capacity of the gamma-Psi-dimensions to take into account the specificities of a classifier.

Determinantal point processes (DPPs) are specific probability distributions over clouds of points that are used as models and computational tools across physics, probability, statistics, and more recently machine learning. Sampling from DPPs is a challenge and therefore we present DPPy, a Python toolbox that gathers known exact and approximate sampling algorithms. The project is hosted on GitHub and equipped with an extensive documentation. This documentation takes the form of a short survey of DPPs and relates each mathematical property with DPPy objects.

Linear regression models contaminated by Gaussian noise (inlier) and possibly unbounded sparse outliers are common in many signal processing applications. Sparse recovery inspired robust regression (SRIRR) techniques are shown to deliver high quality estimation performance in such regression models. Unfortunately, most SRIRR techniques assume \textit{a priori} knowledge of noise statistics like inlier noise variance or outlier statistics like number of outliers. Both inlier and outlier noise statistics are rarely known \textit{a priori} and this limits the efficient operation of many SRIRR algorithms. This article proposes a novel noise statistics oblivious algorithm called residual ratio thresholding GARD (RRT-GARD) for robust regression in the presence of sparse outliers. RRT-GARD is developed by modifying the recently proposed noise statistics dependent greedy algorithm for robust de-noising (GARD). Both finite sample and asymptotic analytical results indicate that RRT-GARD performs nearly similar to GARD with \textit{a priori} knowledge of noise statistics. Numerical simulations in real and synthetic data sets also point to the highly competitive performance of RRT-GARD.

The goal of system identification is to learn about underlying physics dynamics behind the observed time-series data. To model the nonparametric and probabilistic dynamics model, Gaussian process state-space models (GPSSMs) have been widely studied; GPs are not only capable to represent nonlinear dynamics, but estimate the uncertainty of prediction and avoid over-fitting. Traditional GPSSMs, however, are based on Gaussian transition model, thus often have difficulty in describing multi-modal motions. To resolve the challenge, this thesis proposes a model using multiple GPs and extends the GPSSM to information-theoretic framework by introducing a mutual information regularizer helping the model to learn interpretable and disentangled representation of multi-modal transition dynamics model. Experiment results show that the proposed model not only successfully represents the observed system but distinguishes the dynamics mode that governs the given observation sequence.

Multi-task learning (MTL) refers to the paradigm of learning multiple related tasks together. By contrast, single-task learning (STL) learns each individual task independently. MTL often leads to better trained models because they can leverage the commonalities among related tasks. However, because MTL algorithms will "transmit" information on different models across different tasks, MTL poses a potential security risk. Specifically, an adversary may participate in the MTL process through a participating task, thereby acquiring the model information for another task. Previously proposed privacy-preserving MTL methods protect data instances rather than models, and some of them may underperform in comparison with STL methods. In this paper, we propose a privacy-preserving MTL framework to prevent the information on each model from leaking to other models based on a perturbation of the covariance matrix of the model matrix, and we study two popular MTL approaches for instantiation, namely, MTL approaches for learning the low-rank and group-sparse patterns of the model matrix. Our methods are built upon tools for differential privacy. Privacy guarantees and utility bounds are provided. Heterogeneous privacy budgets are considered. Our algorithms can be guaranteed not to underperform comparing with STL methods. Experiments demonstrate that our algorithms outperform existing privacy-preserving MTL methods on the proposed model-protection problem.

This paper summarizes the work of building the autonomous system including detection system and path tracking controller for a formula student autonomous racecar. A LIDAR-vision cooperating method of detecting traffic cone which is used as track mark is proposed. Detection algorithm of the racecar also implements a precise and high rate localization method which combines the GPS-INS data and LIDAR odometry. Besides, a track map including the location and color information of the cones is built simultaneously. Finally, the system and vehicle performance on a closed loop track is tested. This paper also briefly introduces the Formula Student Autonomous Competition (FSAC) in 2017.

As machine learning systems move from computer-science laboratories into the open world, their accountability becomes a high priority problem. Accountability requires deep understanding of system behavior and its failures. Current evaluation methods such as single-score error metrics and confusion matrices provide aggregate views of system performance that hide important shortcomings. Understanding details about failures is important for identifying pathways for refinement, communicating the reliability of systems in different settings, and for specifying appropriate human oversight and engagement. Characterization of failures and shortcomings is particularly complex for systems composed of multiple machine learned components. For such systems, existing evaluation methods have limited expressiveness in describing and explaining the relationship among input content, the internal states of system components, and final output quality. We present Pandora, a set of hybrid human-machine methods and tools for describing and explaining system failures. Pandora leverages both human and system-generated observations to summarize conditions of system malfunction with respect to the input content and system architecture. We share results of a case study with a machine learning pipeline for image captioning that show how detailed performance views can be beneficial for analysis and debugging.

The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a common occurrence in various machine learning algorithms like generalized least squares, support vector machines, Gaussian process regression and kernel based deep neural networks to name a few. Due to the more general structure of the underlying variational problems, the theory is also relevant to other application areas like optimal control, signal processing and decision making. We present the generalized representer as a unified view for supervised and semi-supervised learning methods, using the theory of linear operators and subspace valued maps. The implications of the theorem are presented with examples of multi input-multi output regression, kernel based deep neural networks, stochastic regression and sparsity learning problems as being special cases in this unified view.