Radar-based road user classification is an important yet still challenging task towards autonomous driving applications. The resolution of conventional automotive radar sensors results in a sparse data representation which is tough to recover by subsequent signal processing. In this article, classifier ensembles originating from a one-vs-one binarization paradigm are enriched by one-vs-all correction classifiers. They are utilized to efficiently classify individual traffic participants and also identify hidden object classes which have not been presented to the classifiers during training. For each classifier of the ensemble an individual feature set is determined from a total set of 98 features. Thereby, the overall classification performance can be improved when compared to previous methods and, additionally, novel classes can be identified much more accurately. Furthermore, the proposed structure allows to give new insights in the importance of features for the recognition of individual classes which is crucial for the development of new algorithms and sensor requirements.

An important problem in machine learning and statistics is to identify features that causally affect the outcome. This is often impossible to do from purely observational data, and a natural relaxation is to identify features that are correlated with the outcome even conditioned on all other observed features. For example, we want to identify that smoking really is correlated with cancer conditioned on demographics. The knockoff procedure is a recent breakthrough in statistics that, in theory, can identify truly correlated features while guaranteeing that the false discovery is limited. The idea is to create synthetic data -- knockoffs -- that captures correlations amongst the features. However there are substantial computational and practical challenges to generating and using knockoffs. This paper makes several key advances that enable knockoff application to be more efficient and powerful. We develop an efficient algorithm to generate valid knockoffs from Bayesian Networks. Then we systematically evaluate knockoff test statistics and develop new statistics with improved power. The paper combines new mathematical guarantees with systematic experiments on real and synthetic data.

We study the convergence of the Expectation-Maximization (EM) algorithm for mixtures of linear regressions with an arbitrary number $k$ of components. We show that as long as signal-to-noise ratio (SNR) is more than $\tilde{O}(k^2)$, well-initialized EM converges to the true regression parameters. Previous results for $k \geq 3$ have only established local convergence for the noiseless setting, i.e., where SNR is infinitely large. Our results establish a near optimal statistical error rate of $\tilde{O}(\sigma \sqrt{k^2 d/n})$ for (sample-splitting) finite-sample EM with $k$ components, where $d$ is dimension, $n$ is the number of samples, and $\sigma$ is the variance of noise. In particular, our results imply exact recovery as $\sigma \rightarrow 0$, in contrast to most previous local convergence results for EM, where the statistical error scaled with the norm of parameters. Standard moment-method approaches suffice to guarantee we are in the region where our local convergence guarantees apply.

We introduce a new regularization-based continual learning algorithm, dubbed as Uncertainty-regularized Continual Learning (UCL), that stores much smaller number of additional parameters for regularization terms than the recent state-of-the-art methods. Our approach builds upon the Bayesian learning framework, but makes a fresh interpretation of the variational approximation based regularization term and defines a notion of "uncertainty" for each hidden node in the network. The regularization parameter of each weight is then set to be large when the uncertainty of either of the node that the weight connects is small, since the weights connected to an important node should be less updated when a new task comes. Moreover, we add two additional regularization terms; one that promotes freezing the weights that are identified to be important (i.e., certain) for past tasks, and the other that gives flexibility to control the actively learning parameters for a new task by gracefully forgetting what was learned before. In results, we show our UCL outperforms most of recent state-of-the-art baselines on both supervised learning and reinforcement learning benchmarks.

In this work we present novel differentially private identity (goodness-of-fit) testers for natural and widely studied classes of multivariate product distributions: Gaussians in $\mathbb{R}^d$ with known covariance and product distributions over $\{\pm 1\}^{d}$. Our testers have improved sample complexity compared to those derived from previous techniques, and are the first testers whose sample complexity matches the order-optimal minimax sample complexity of $O(d^{1/2}/\alpha^2)$ in many parameter regimes. We construct two types of testers, exhibiting tradeoffs between sample complexity and computational complexity. Finally, we provide a two-way reduction between testing a subclass of multivariate product distributions and testing univariate distributions, and thereby obtain upper and lower bounds for testing this subclass of product distributions.

Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide explanations that help the affected individuals not only to understand why a prediction was output, but also how to act to obtain a desired outcome. To this end, several works have proposed methods to generate counterfactual explanations. However, they are often restricted to a particular subset of models (e.g., decision trees or linear models), and cannot directly handle the mixed (numerical and nominal) nature of the features describing each individual. In this paper, we propose a model-agnostic algorithm to generate counterfactual explanations that builds on the standard theory and tools from formal verification. Specifically, our algorithm solves a sequence of satisfiability problems, where a wide variety of predictive models and distances in mixed feature spaces, as well as natural notions of plausibility and diversity, are represented as logic formulas. Our experiments on real-world data demonstrate that our approach can flexibly handle widely deployed predictive models, while providing meaningfully closer counterfactuals than existing approaches.

Many recent works have shown that adversarial examples that fool classifiers can be found by minimally perturbing a normal input. Recent theoretical results, starting with Gilmer et al. (2018), show that if the inputs are drawn from a concentrated metric probability space, then adversarial examples with small perturbation are inevitable. A concentrated space has the property that any subset with $\Omega(1)$ (e.g., 1/100) measure, according to the imposed distribution, has small distance to almost all (e.g., 99/100) of the points in the space. It is not clear, however, whether these theoretical results apply to actual distributions such as images. This paper presents a method for empirically measuring and bounding the concentration of a concrete dataset which is proven to converge to the actual concentration. We use it to empirically estimate the intrinsic robustness to $\ell_\infty$ and $\ell_2$ perturbations of several image classification benchmarks.

We present a fast and scalable algorithm to induce non-monotonic logic programs from statistical learning models. We reduce the problem of search for best clauses to instances of the High-Utility Itemset Mining (HUIM) problem. In the HUIM problem, feature values and their importance are treated as transactions and utilities respectively. We make use of TreeExplainer, a fast and scalable implementation of the Explainable AI tool SHAP, to extract locally important features and their weights from ensemble tree models. Our experiments with UCI standard benchmarks suggest a significant improvement in terms of classification evaluation metrics and running time of the training algorithm compared to ALEPH, a state-of-the-art Inductive Logic Programming (ILP) system.

The convergence of many reinforcement learning (RL) algorithms with linear function approximation has been investigated extensively but most proofs assume that these methods converge to a unique solution. In this paper, we provide a complete characterization of non-uniqueness issues for a large class of reinforcement learning algorithms, simultaneously unifying many counter-examples to convergence in a theoretical framework. We achieve this by proving a new condition on features that can determine whether the convergence assumptions are valid or non-uniqueness holds. We consider a general class of RL methods, which we call natural algorithms, whose solutions are characterized as the fixed point of a projected Bellman equation (when it exists); notably, bootstrapped temporal difference-based methods such as $TD(\lambda)$ and $GTD(\lambda)$ are natural algorithms. Our main result proves that natural algorithms converge to the correct solution if and only if all the value functions in the approximation space satisfy a certain shape. This implies that natural algorithms are, in general, inherently prone to converge to the wrong solution for most feature choices even if the value function can be represented exactly. Given our results, we show that state aggregation based features are a safe choice for natural algorithms and we also provide a condition for finding convergent algorithms under other feature constructions.

We propose GraphNVP, the first invertible, normalizing flow-based molecular graph generation model. We decompose the generation of a graph into two steps: generation of (i) an adjacency tensor and (ii) node attributes. This decomposition yields the exact likelihood maximization on graph-structured data, combined with two novel reversible flows. We empirically demonstrate that our model efficiently generates valid molecular graphs with almost no duplicated molecules. In addition, we observe that the learned latent space can be used to generate molecules with desired chemical properties.