We propose a new classifier based on Dempster-Shafer (DS) theory and a convolutional neural network (CNN) architecture for set-valued classification. In this classifier, called the evidential deep-learning classifier, convolutional and pooling layers first extract high-dimensional features from input data. The features are then converted into mass functions and aggregated by Dempster's rule in a DS layer. Finally, an expected utility layer performs set-valued classification based on mass functions. We propose an end-to-end learning strategy for jointly updating the network parameters. Additionally, an approach for selecting partial multi-class acts is proposed. Experiments on image recognition, signal processing, and semantic-relationship classification tasks demonstrate that the proposed combination of deep CNN, DS layer, and expected utility layer makes it possible to improve classification accuracy and to make cautious decisions by assigning confusing patterns to multi-class sets.

We propose a hybrid architecture composed of a fully convolutional network (FCN) and a Dempster-Shafer layer for image semantic segmentation. In the so-called evidential FCN (E-FCN), an encoder-decoder architecture first extracts pixel-wise feature maps from an input image. A Dempster-Shafer layer then computes mass functions at each pixel location based on distances to prototypes. Finally, a utility layer performs semantic segmentation from mass functions and allows for imprecise classification of ambiguous pixels and outliers. We propose an end-to-end learning strategy for jointly updating the network parameters, which can make use of soft (imprecise) labels. Experiments using three databases (Pascal VOC 2011, MIT-scene Parsing and SIFT Flow) show that the proposed combination improves the accuracy and calibration of semantic segmentation by assigning confusing pixels to multi-class sets.

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.

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.

When linear models are fit to ill-conditioned or confounded narrow-data, TRACE plots are useful in demonstrating and justifying deliberately biased estimation. This makes TRACE diagnostics powerful "visual" displays. If advanced students of regression are trained in interpretation of Trace plots, they could help admininstrators capable of basic statistical thinking avoid misinterpretations of questionable regression coefficient estimates. All five types of ridge TRACE plots for a wide variety of ridge paths can be explored using R-functions. For example, the RXshrink aug.lars() function generates TRACE s for Least-Angle, Lasso and Forward Stagewise methods (Efron, Hastie, Johnstone and Tibshirani 2004; Hastie and

TL;DR: motivated to better understand the fundamental tradeoffs in federated learning, we present a probabilistic perspective that generalizes and improves upon federated optimization and enables a new class of efficient federated learning algorithms. Thanks to deep learning, today we can train better machine learning models when given access to massive data. However, the standard, centralized training is impossible in many interesting use-cases--due to the associated data transfer and maintenance costs (most notably in video analytics), privacy concerns (e.g., in healthcare settings), or sensitivity of the proprietary data (e.g., in drug discovery). And yet, different parties that own even a small amount of data want to benefit from access to accurate models. This is where federated learning comes to the rescue!

Approximating optimal policies in reinforcement learning (RL) is often necessary in many real-world scenarios, which is termed as policy optimization. By viewing the reinforcement learning from the perspective of variational inference (VI), the policy network is trained to obtain the approximate posterior of actions given the optimality criteria. However, in practice, the policy optimization may lead to suboptimal policy estimates due to the amortization gap and insufficient exploration. In this work, inspired by the previous use of Hamiltonian Monte Carlo (HMC) in VI, we propose to integrate policy optimization with HMC. As such we choose evolving actions from the base policy according to HMC. First, HMC can improve the policy distribution to better approximate the posterior and hence reduces the amortization gap. Second, HMC can also guide the exploration more to the regions with higher action values, enhancing the exploration efficiency. Instead of directly applying HMC into RL, we propose a new leapfrog operator to simulate the Hamiltonian dynamics. With comprehensive empirical experiments on continuous control baselines, including MuJoCo, PyBullet Roboschool and DeepMind Control Suite, we show that the proposed approach is a data-efficient, and an easy-to-implement improvement over previous policy optimization methods. Besides, the proposed approach can also outperform previous methods on DeepMind Control Suite, which has image-based high-dimensional observation space.