We study active structure learning of Bayesian networks in an observational setting, in which there are external limitations on the number of variable values that can be observed from the same sample. Random samples are drawn from the joint distribution of the network variables, and the algorithm iteratively selects which variables to observe in the next sample. We propose a new active learning algorithm for this setting, that finds with a high probability a structure with a score that is $\epsilon$-close to the optimal score. We show that for a class of distributions that we term stable, a sample complexity reduction of up to a factor of $\widetilde{\Omega}(d^3)$ can be obtained, where $d$ is the number of network variables. We further show that in the worst case, the sample complexity of the active algorithm is guaranteed to be almost the same as that of a naive baseline algorithm. To supplement the theoretical results, we report experiments that compare the performance of the new active algorithm to the naive baseline and demonstrate the sample complexity improvements. Code for the algorithm and for the experiments is provided at https://github.com/noabdavid/activeBNSL.

The field of meta-learning seeks to improve the ability of today's machine learning systems to adapt efficiently to small amounts of data. Typically this is accomplished by training a system with a parametrized update rule to improve a task-relevant objective based on supervision or a reward function. However, in many domains of practical interest, task data is unlabeled, or reward functions are unavailable. In this paper we introduce a new approach to address the more general problem of generative meta-learning, which we argue is an important prerequisite for obtaining human-level cognitive flexibility in artificial agents, and can benefit many practical applications along the way. Our contribution leverages the AEVB framework and mean-field variational Bayes, and creates fast-adapting latent-space generative models. At the heart of our contribution is a new result, showing that for a broad class of deep generative latent variable models, the relevant VB updates do not depend on any generative neural network. The theoretical merits of our approach are reflected in empirical experiments.

We introduce the problem of robust subgroup discovery, i.e., finding a set of interpretable descriptions of subsets that 1) stand out with respect to one or more target attributes, 2) are statistically robust, and 3) non-redundant. Many attempts have been made to mine either locally robust subgroups or to tackle the pattern explosion, but we are the first to address both challenges at the same time from a global perspective. First, we formulate a broad model class of subgroup lists, i.e., ordered sets of subgroups, for univariate and multivariate targets that can consist of nominal or numeric variables. This novel model class allows us to formalize the problem of optimal robust subgroup discovery using the Minimum Description Length (MDL) principle, where we resort to optimal Normalized Maximum Likelihood and Bayesian encodings for nominal and numeric targets, respectively. Notably, we show that our problem definition is equal to mining the top-1 subgroup with an information-theoretic quality measure plus a penalty for complexity. Second, as finding optimal subgroup lists is NP-hard, we propose RSD, a greedy heuristic that finds good subgroup lists and guarantees that the most significant subgroup found according to the MDL criterion is added in each iteration, which is shown to be equivalent to a Bayesian one-sample proportions, multinomial, or t-test between the subgroup and dataset marginal target distributions plus a multiple hypothesis testing penalty. We empirically show on 54 datasets that RSD outperforms previous subgroup set discovery methods in terms of quality and subgroup list size.

The paper formalizes constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We define a "generic" structure learning algorithm, which provides conditions that, under the faithfulness assumption, the output of all known exact algorithms in the literature must satisfy, and which outputs graphs that are Markov equivalent to the causal graph. More importantly, we provide clear assumptions, weaker than faithfulness, under which the same generic algorithm outputs Markov equivalent graphs to the causal graph. We provide the theory for the general class of models under the assumption that the distribution is Markovian to the true causal graph, and we specialize the definitions and results for structural causal models.

We will discuss how over the last 30 to 50 years, systems that focused only on data have been handicapped with success focused on narrowly focused tasks, and knowledge has been critical in developing smarter, intelligent, more effective systems. We will draw a parallel with the role of knowledge and experience in human intelligence based on cognitive science. And we will end with the recent interest in neuro-symbolic or hybrid AI systems in which knowledge is the critical enabler for combining data-intensive statistical AI systems with symbolic AI systems which results in more capable AI systems that support more human-like intelligence.

In this work, we study the problem of user preference learning on the example of parameter setting for a hearing aid (HA). We propose to use an agent that interacts with a HA user, in order to collect the most informative data, and learns user preferences for HA parameter settings, based on these data. We model the HA system as two interacting sub-systems, one representing a user with his/her preferences and another one representing an agent. In this system, the user responses to HA settings, proposed by the agent. In our user model, the responses are driven by a parametric user preference function. The agent comprises the sequential mechanisms for user model inference and HA parameter proposal generation. To infer the user model (preference function), Bayesian approximate inference is used in the agent. Here we propose the normalized weighted Kullback-Leibler (KL) divergence between true and agent-assigned predictive user response distributions as a metric to assess the quality of learned preferences. Moreover, our agent strategy for generating HA parameter proposals is to generate HA settings, responses to which help resolving uncertainty associated with prediction of the user responses the most. The resulting data, consequently, allows for efficient user model learning. The normalized weighted KL-divergence plays an important role here as well, since it characterizes the informativeness of the data to be used for probing the user. The efficiency of our approach is validated by numerical simulations.

Model predictive control (MPC) schemes have a proven track record for delivering aggressive and robust performance in many challenging control tasks, coping with nonlinear system dynamics, constraints, and observational noise. Despite their success, these methods often rely on simple control distributions, which can limit their performance in highly uncertain and complex environments. MPC frameworks must be able to accommodate changing distributions over system parameters, based on the most recent measurements. In this paper, we devise an implicit variational inference algorithm able to estimate distributions over model parameters and control inputs on-the-fly. The method incorporates Stein Variational gradient descent to approximate the target distributions as a collection of particles, and performs updates based on a Bayesian formulation. This enables the approximation of complex multi-modal posterior distributions, typically occurring in challenging and realistic robot navigation tasks. We demonstrate our approach on both simulated and real-world experiments requiring real-time execution in the face of dynamically changing environments.

Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a symbolic-dynamics inspired approach. Under this umbrella, Markov modeling of time-series data consists of two major steps -- discretization of continuous attributes followed by estimating the size of temporal memory of the discretized sequence. These two steps are critical for the accurate and concise representation of time-series data in the discrete space. Discretization governs the information content of the resultant discretized sequence. On the other hand, memory estimation of the symbolic sequence helps to extract the predictive patterns in the discretized data. Clearly, the effectiveness of signal representation as a discrete Markov process depends on both these steps. In this paper, we will review the different techniques for discretization and memory estimation for discrete stochastic processes. In particular, we will focus on the individual problems of discretization and order estimation for discrete stochastic process. We will present some results from literature on partitioning from dynamical systems theory and order estimation using concepts of information theory and statistical learning. The paper also presents some related problem formulations which will be useful for machine learning and statistical learning application using the symbolic framework of data analysis. We present some results of statistical analysis of a complex thermoacoustic instability phenomenon during lean-premixed combustion in jet-turbine engines using the proposed Markov modeling method.

The technique aims to fix the logic of the network at an intermediate layer or at the last layer. NNrepair first uses fault localization to find potentially faulty network parameters (such as the weights) and then performs repair using constraint solving to apply small modifications to the parameters to remedy the defects. We present novel strategies to enable precise yet efficient repair such as inferring correctness specifications to act as oracles for intermediate layer repair, and generation of experts for each class. We demonstrate the technique in the context of three different scenarios: (1) Improving the overall accuracy of a model, (2) Fixing security vulnerabilities caused by poisoning of training data and (3) Improving the robustness of the network against adversarial attacks. Our evaluation on MNIST and CIFAR-10 models shows that NNrepair can improve the accuracy by 45.56 percentage points on poisoned data and 10.40 percentage points on adversarial data. NNrepair also provides small improvement in the overall accuracy of models, without requiring new data or re-training.

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian processes. The proposed approach (1) provides a natural generalization of collocation kernel methods to nonlinear PDEs and IPs, (2) has guaranteed convergence with a path to compute error bounds in the PDE setting, and (3) inherits the state-of-the-art computational complexity of linear solvers for dense kernel matrices. The main idea of our method is to approximate the solution of a given PDE with a MAP estimator of a Gaussian process given the observation of the PDE at a finite number of collocation points. Although this optimization problem is infinite-dimensional, it can be reduced to a finite-dimensional one by introducing additional variables corresponding to the values of the derivatives of the solution at collocation points; this generalizes the representer theorem arising in Gaussian process regression. The reduced optimization problem has a quadratic loss and nonlinear constraints, and it is in turn solved with a variant of the Gauss-Newton method. The resulting algorithm (a) can be interpreted as solving successive linearizations of the nonlinear PDE, and (b) is found in practice to converge in a small number (two to ten) of iterations in experiments conducted on a range of PDEs. For IPs, while the traditional approach has been to iterate between the identifications of parameters in the PDE and the numerical approximation of its solution, our algorithm tackles both simultaneously. Experiments on nonlinear elliptic PDEs, Burgers' equation, a regularized Eikonal equation, and an IP for permeability identification in Darcy flow illustrate the efficacy and scope of our framework.