Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schr\"odinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions, the Schr\"odinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa. This allows us to apply methods developed for the analysis of high-dimensional stochastic differential equations to quantum mechanical systems.

Automated machine learning (AutoML) can produce complex model ensembles by stacking, bagging, and boosting many individual models like trees, deep networks, and nearest neighbor estimators. While highly accurate, the resulting predictors are large, slow, and opaque as compared to their constituents. To improve the deployment of AutoML on tabular data, we propose FAST-DAD to distill arbitrarily complex ensemble predictors into individual models like boosted trees, random forests, and deep networks. At the heart of our approach is a data augmentation strategy based on Gibbs sampling from a self-attention pseudolikelihood estimator. Across 30 datasets spanning regression and binary/multiclass classification tasks, FAST-DAD distillation produces significantly better individual models than one obtains through standard training on the original data. Our individual distilled models are over 10x faster and more accurate than ensemble predictors produced by AutoML tools like H2O/AutoSklearn.

The option framework has shown great promise by automatically extracting temporally-extended sub-tasks from a long-horizon task. Methods have been proposed for concurrently learning low-level intra-option policies and high-level option selection policy. However, existing methods typically suffer from two major challenges: ineffective exploration and unstable updates. In this paper, we present a novel and stable off-policy approach that builds on the maximum entropy model to address these challenges. Our approach introduces an information-theoretical intrinsic reward for encouraging the identification of diverse and effective options. Meanwhile, we utilize a probability inference model to simplify the optimization problem as fitting optimal trajectories. Experimental results demonstrate that our approach significantly outperforms prior on-policy and off-policy methods in a range of Mujoco benchmark tasks while still providing benefits for transfer learning. In these tasks, our approach learns a diverse set of options, each of whose state-action space has strong coherence.

To account for the sequential and nonconvex nature, new solution concepts and algorithms have been developed. In this work, we provide a detailed analysis of existing algorithms and relate them to two novel Newton-type algorithms. We argue that our Newton-type algorithms nicely complement existing ones in that (a) they converge faster to (strict) local minimax points; (b) they are much more effective when the problem is ill-conditioned; (c) their computational complexity remains similar. We verify our theoretical results by conducting experiments on training GANs.

Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such trade-off is often hard to achieve since we lack human-independent interpretability metrics. We introduce a novel sequence learning algorithm, that combines (i) linear classifiers - which are known to strike a good balance between predictive power and interpretability, and (ii) background knowledge embeddings. We extend the classic subsequence feature space with groups of symbols which are generated by background knowledge injected via word or graph embeddings, and use this new feature space to learn a linear classifier. We also present a new measure to evaluate the interpretability of a set of symbolic features based on the symbol embeddings. Experiments on human activity recognition from wearables and amino acid sequence classification show that our classification approach preserves predictive power, while delivering more interpretable models.

We describe an R package named huge which provides easy-to-use functions for estimating high dimensional undirected graphs from data. This package implements recent results in the literature, including Friedman et al. (2007), Liu et al. (2009, 2012) and Liu et al. (2010). Compared with the existing graph estimation package glasso, the huge package provides extra features: (1) instead of using Fortan, it is written in C, which makes the code more portable and easier to modify; (2) besides fitting Gaussian graphical models, it also provides functions for fitting high dimensional semiparametric Gaussian copula models; (3) more functions like data-dependent model selection, data generation and graph visualization; (4) a minor convergence problem of the graphical lasso algorithm is corrected; (5) the package allows the user to apply both lossless and lossy screening rules to scale up large-scale problems, making a tradeoff between computational and statistical efficiency.

Adversarial poisoning attacks distort training data in order to corrupt the test-time behavior of a classifier. A provable defense provides a certificate for each test sample, which is a lower bound on the magnitude of any adversarial distortion of the training set that can corrupt the test sample's classification. We propose two provable defenses against poisoning attacks: (i) Deep Partition Aggregation (DPA), a certified defense against a general poisoning threat model, defined as the insertion or deletion of a bounded number of samples to the training set -- by implication, this threat model also includes arbitrary distortions to a bounded number of images and/or labels; and (ii) Semi-Supervised DPA (SS-DPA), a certified defense against label-flipping poisoning attacks. DPA is an ensemble method where base models are trained on partitions of the training set determined by a hash function. DPA is related to subset aggregation, a well-studied ensemble method in classical machine learning. DPA can also be viewed as an extension of randomized ablation (Levine & Feizi, 2020a), a certified defense against sparse evasion attacks, to the poisoning domain. Our label-flipping defense, SS-DPA, uses a semi-supervised learning algorithm as its base classifier model: we train each base classifier using the entire unlabeled training set in addition to the labels for a partition. SS-DPA outperforms the existing certified defense for label-flipping attacks (Rosenfeld et al., 2020). SS-DPA certifies >= 50% of test images against 675 label flips (vs. < 200 label flips with the existing defense) on MNIST and 83 label flips on CIFAR-10. Against general poisoning attacks (no prior certified defense), DPA certifies >= 50% of test images against > 500 poison image insertions on MNIST, and nine insertions on CIFAR-10. These results establish new state-of-the-art provable defenses against poison attacks.

Conditional Value at Risk (CVaR) is a family of "coherent risk measures" which generalize the traditional mathematical expectation. Widely used in mathematical finance, it is garnering increasing interest in machine learning, e.g., as an alternate approach to regularization, and as a means for ensuring fairness. This paper presents a generalization bound for learning algorithms that minimize the CVaR of the empirical loss. The bound is of PAC-Bayesian type and is guaranteed to be small when the empirical CVaR is small. We achieve this by reducing the problem of estimating CVaR to that of merely estimating an expectation. This then enables us, as a by-product, to obtain concentration inequalities for CVaR even when the random variable in question is unbounded.

The proliferation of medical monitoring devices makes it possible to track health vitals at high frequency, enabling the development of dynamic health risk scores that change with the underlying readings. Survival analysis, in particular hazard estimation, is well-suited to analyzing this stream of data to predict disease onset as a function of the time-varying vitals. This paper introduces the software package BoXHED (pronounced 'box-head') for nonparametrically estimating hazard functions via gradient boosting. BoXHED 1.0 is a novel tree-based implementation of the generic estimator proposed in Lee, Chen, Ishwaran (2017), which was designed for handling time-dependent covariates in a fully nonparametric manner. BoXHED is also the first publicly available software implementation for Lee, Chen, Ishwaran (2017). Applying BoXHED to cardiovascular disease onset data from the Framingham Heart Study reveals novel interaction effects among known risk factors, potentially resolving an open question in clinical literature.

Gradient-based meta-learning (GBML) with deep neural nets (DNNs) has become a popular approach for few-shot learning. However, due to the non-convexity of DNNs and the complex bi-level optimization in GBML, the theoretical properties of GBML with DNNs remain largely unknown. In this paper, we first develop a novel theoretical analysis to answer the following questions: Does GBML with DNNs have global convergence guarantees? We provide a positive answer to this question by proving that GBML with over-parameterized DNNs is guaranteed to converge to global optima at a linear rate. The second question we aim to address is: How does GBML achieve fast adaption to new tasks with experience on past similar tasks? To answer it, we prove that GBML is equivalent to a functional gradient descent operation that explicitly propagates experience from the past tasks to new ones. Finally, inspired by our theoretical analysis, we develop a new kernel-based meta-learning approach. We show that the proposed approach outperforms GBML with standard DNNs on the Omniglot dataset when the number of past tasks for meta-training is small. The code is available at https://github.com/ AI-secure/Meta-Neural-Kernel .