General Motors is inching closer to self-driving vehicles with the introduction of a new feature that will enable some Cadillacs to change lanes on their own. GM announced Tuesday it's upgrading its Super Cruise system to enable automated lane changing. The technology will safely change lanes when drivers signal they'd like to do so. Super Cruise already enables hands-free driving on fully mapped highways. It keeps the car centered in its lane, brakes, accelerates and notifies drivers when they must take over the controls.

Amid the fear and intrigue surrounding the coronavirus, people are downloading a simulation video game in which players use real-time strategy to spread a deadly outbreak around the world. The video game's developers warn people not to take the game too seriously and to seek advice about how epidemics travel from authoritative sources. The coronavirus has sickened more than 4,500 people and killed more than 100. The illness originated in China before moving to other parts of the globe, including the USA. Plague Inc. is an 8-year-old app and PC game in which users play the role of a disease intent on infecting the world with a pathogen.

Gaussian processes are ubiquitous in statistical analysis, machine learning and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying our uncertainty about this task in a computationally tractable manner. An important question is whether these approximations will be accurate, and if so how accurate, given our various modelling choices and the difficulty of the problem. This is of practical relevance, since the answer informs our choice of model and sampling distribution for a given application. Our paper provides novel approximation guarantees for Gaussian process models based on covariance functions with finite smoothness, such as the Mat\'ern and Wendland covariance functions. They are derived from a sampling inequality which facilitates a systematic approach to obtaining upper bounds on Sobolev norms in terms of properties of the design used to collect data. This approach allows us to refine some existing results which apply in the misspecified smoothness setting and which allow for adaptive selection of hyperparameters. However, the main novelty in this paper is that our results cover a wide range of observation models including interpolation, approximation with deterministic corruption and regression with Gaussian noise.

Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides one of the first theoretical analyses in the context of Gaussian process regression with a noiseless dataset. Specifically, we consider the scenario where the scale parameter of a Sobolev kernel (such as a Mat\'ern kernel) is estimated by maximum likelihood. We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model in the sense that the model can become "slowly" overconfident at worst, regardless of the difference between the smoothness of the data-generating function and that expected by the model. The analysis is based on a combination of techniques from nonparametric regression and scattered data interpolation. Empirical results are provided in support of the theoretical findings.

Such models have been shown to allow estimation and inference by regression clustering methods. This paper is motivated by the finding that the clustered heterogeneity models studied in this literature can be badly misspecified, even when the panel has significant discrete cross-sectional structure. To address this issue, we generalize previous approaches to discrete unobserved heterogeneity by allowing each unit to have multiple, imperfectly-correlated latent variables that describe its response-type to different covariates. We give inference results for a k-means style estimator of our model and develop information criteria to jointly select the number clusters for each latent variable. Monte Carlo simulations confirm our theoretical results and give intuition about the finite-sample performance of estimation and model selection. We also contribute to the theory of clustering with an over-specified number of clusters and derive new convergence rates for this setting. Our results suggest that over-fitting can be severe in k-means style estimators when the number of clusters is over-specified.

Ubiquitous systems with End-Edge-Cloud architecture are increasingly being used in healthcare applications. Federated Learning (FL) is highly useful for such applications, due to silo effect and privacy preserving. Existing FL approaches generally do not account for disparities in the quality of local data labels. However, the clients in ubiquitous systems tend to suffer from label noise due to varying skill-levels, biases or malicious tampering of the annotators. In this paper, we propose Federated Opportunistic Computing for Ubiquitous Systems (FOCUS) to address this challenge. It maintains a small set of benchmark samples on the FL server and quantifies the credibility of the client local data without directly observing them by computing the mutual cross-entropy between performance of the FL model on the local datasets and that of the client local FL model on the benchmark dataset. Then, a credit weighted orchestration is performed to adjust the weight assigned to clients in the FL model based on their credibility values. FOCUS has been experimentally evaluated on both synthetic data and real-world data. The results show that it effectively identifies clients with noisy labels and reduces their impact on the model performance, thereby significantly outperforming existing FL approaches.

Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions. In the former, we may require the prediction model to respect the presence of physical paths between the nodes on the map, and in the latter, we may require that the prediction model respect fairness constraints that ensure that outcomes are not subject to bias. Broadly speaking, constraints may be probabilistic, logical or causal, but the overarching challenge is to determine if and how a model can be learnt that handles all the declared constraints. To the best of our knowledge, this is largely an open problem. In this paper, we consider a mathematical inquiry on how the learning of tractable probabilistic models, such as sum-product networks, is possible while incorporating constraints.

Algorithm selection (AS) deals with selecting an algorithm from a fixed set of candidate algorithms most suitable for a specific instance of an algorithmic problem, e.g., choosing solvers for SA T problems. Benchmark suites for AS usually comprise candidate sets consisting of at most tens of algorithms, whereas in combined algorithm selection and hyperparameter optimization problems the number of candidates becomes intractable, impeding to learn effective meta-models and thus requiring costly online performance evaluations. Therefore, here we propose the setting of extreme algorithm selection (XAS) where we consider fixed sets of thousands of candidate algorithms, facilitating meta learning. W e assess the applicability of state-of-the-art AS techniques to the XAS setting and propose approaches leveraging a dyadic feature representation in which both problem instances and algorithms are described. W e find the latter to improve significantly over the current state of the art in various metrics.

We introduce gym-city, a Reinforcement Learning environment that uses SimCity 1's game engine to simulate an urban environment, wherein agents might seek to optimize one or a combination of any number of city-wide metrics, on gameboards of various sizes. We focus on population, and analyze our agents' ability to generalize to larger map-sizes than those seen during training. The environment is interactive, allowing a human player to build alongside agents during training and inference, potentially influencing the course of their learning, or manually probing and evaluating their performance. To test our agents' ability to capture distance-agnostic relationships between elements of the gameboard, we design a minigame within the environment which is, by design, unsolvable at large enough scales given strictly local strategies. Given the game engine's extensive use of Cellular Automata, we also train our agents to "play" Conway's Game of Life -- again optimizing for population -- and examine their behaviour at multiple scales. To make our models compatible with variable-scale gameplay, we use Neural Networks with recursive weights and structure -- fractals to be truncated at different depths, dependent upon the size of the gameboard.

In recent years, significant attention has been devoted towards integrating deep learning technologies in the healthcare domain. However, to safely and practically deploy deep learning models for home health monitoring, two significant challenges must be addressed: the models should be (1) robust against noise; and (2) compact and energy-efficient. We propose REST, a new method that simultaneously tackles both issues via 1) adversarial training and controlling the Lipschitz constant of the neural network through spectral regularization while 2) enabling neural network compression through sparsity regularization. We demonstrate that REST produces highly-robust and efficient models that substantially outperform the original full-sized models in the presence of noise. For the sleep staging task over single-channel electroencephalogram (EEG), the REST model achieves a macro-F1 score of 0.67 vs. 0.39 achieved by a state-of-the-art model in the presence of Gaussian noise while obtaining 19x parameter reduction and 15x MFLOPS reduction on two large, real-world EEG datasets. By deploying these models to an Android application on a smartphone, we quantitatively observe that REST allows models to achieve up to 17x energy reduction and 9x faster inference. We open-source the code repository with this paper: https://github.com/duggalrahul/REST.