Sampling-based model predictive control (MPC) can be applied to versatile robotic systems. However, the real-time control with it is a big challenge due to its unstable updates and poor convergence. This paper tackles this challenge with a novel derivation from reverse Kullback-Leibler divergence, which has a mode-seeking behavior and is likely to find one of the sub-optimal solutions early. With this derivation, a weighted maximum likelihood estimation with positive/negative weights is obtained, solving by mirror descent (MD) algorithm. While the negative weights eliminate unnecessary actions, that requires to develop a practical implementation that avoids the interference with positive/negative updates based on rejection sampling. In addition, although the convergence of MD can be accelerated with Nesterov's acceleration method, it is modified for the proposed MPC with a heuristic of a step size adaptive to the noise estimated in update amounts. In the real-time simulations, the proposed method can solve more tasks statistically than the conventional method and accomplish more complex tasks only with a CPU due to the improved acceleration. In addition, its applicability is also demonstrated in a variable impedance control of a force-driven mobile robot. https://youtu.be/D8bFMzct1XM

Regression is often associated with the task of curve fitting -- given data samples for pairs of random variables (X, Y), find a function y = F (x) that captures the relationship between X and Y as well as possible. As the underlying population for the (X, Y) pairs becomes increasingly complex, much efforts have been devoted to learning more complex models for the (regression) function F; see [20, 49, 15] for some recent examples. In many data domains, however, due to the heterogeneity of the behavior of the response variable Y with respect to covariate X, no single function F can fit the data pairs well, no matter how complex F is. Many authors noticed this challenge and adopted a mixture modeling framework into the regression problem, starting with some earlier work of [51, 6, 14]. To capture the uncertain and highly heterogeneous behavior of response variable Y given covariate X, one needs more than one single regression model. Suppose that there are k different regression behaviors, one can represent the conditional distribution of Y given X by a mixture of k conditional density functions associated with k underlying (latent) subpopulations. One can draw from the existing modeling tools of conditional densities such as generalized linear models [39], or more complex components [28, 63, 22] to increase the model fitness for the regression task. Recently, mixture of regression models (alternatively, regression mixture models) have found their applications in a vast range of domains, including risk estimation [2], education [7], medicine [34, 43, 56] and transportation analysis [46, 47, 64]. Making inferences in mixture of regression models can be done in a classical frequentist framework (e.g., maximum conditional likelihood estimation [6]), or a Bayesian framework [27].

Bayesian networks (BNs) are attractive, because they are graphical and interpretable machine learning models. However, exact inference on BNs is time-consuming, especially for complex problems. To improve the efficiency, we propose a fast BN exact inference solution named Fast-BNI on multi-core CPUs. Fast-BNI enhances the efficiency of exact inference through hybrid parallelism that tightly integrates coarse- and fine-grained parallelism. We also propose techniques to further simplify the bottleneck operations of BN exact inference. Fast-BNI source code is freely available at https://github.com/jjiantong/FastBN.

This paper proposes a novel multivariate definition of statistical dependence using a functional methodology inspired by Alfred R\'enyi. We define a new symmetric and self-adjoint cross density kernel through a recursive bidirectional statistical mapping between conditional densities of continuous random processes, which estimates their statistical dependence. Therefore, the kernel eigenspectrum is proposed as a new multivariate statistical dependence measure, and the formulation requires fewer assumptions about the data generation model than current methods. The measure can also be estimated from realizations. The proposed functional maximum correlation algorithm (FMCA) is applied to a learning architecture with two multivariate neural networks. The FMCA optimal solution is an equilibrium point that estimates the eigenspectrum of the cross density kernel. Preliminary results with synthetic data and medium size image datasets corroborate the theory. Four different strategies of applying the cross density kernel are thoroughly discussed and implemented to show the versatility and stability of the methodology, and it transcends supervised learning. When two random processes are high-dimensional real-world images and white uniform noise, respectively, the algorithm learns a factorial code i.e., the occurrence of a code guarantees that a certain input in the training set was present, which is quite important for feature learning.

Bayesian networks (BNs) are a widely used graphical model in machine learning for representing knowledge with uncertainty. The mainstream BN structure learning methods require performing a large number of conditional independence (CI) tests. The learning process is very time-consuming, especially for high-dimensional problems, which hinders the adoption of BNs to more applications. Existing works attempt to accelerate the learning process with parallelism, but face issues including load unbalancing, costly atomic operations and dominant parallel overhead. In this paper, we propose a fast solution named Fast-BNS on multi-core CPUs to enhance the efficiency of the BN structure learning. Fast-BNS is powered by a series of efficiency optimizations including (i) designing a dynamic work pool to monitor the processing of edges and to better schedule the workloads among threads, (ii) grouping the CI tests of the edges with the same endpoints to reduce the number of unnecessary CI tests, (iii) using a cache-friendly data storage to improve the memory efficiency, and (iv) generating the conditioning sets on-the-fly to avoid extra memory consumption. A comprehensive experimental study shows that the sequential version of Fast-BNS is up to 50 times faster than its counterpart, and the parallel version of Fast-BNS achieves 4.8 to 24.5 times speedup over the state-of-the-art multi-threaded solution. Moreover, Fast-BNS has a good scalability to the network size as well as sample size. Fast-BNS source code is freely available at https://github.com/jjiantong/FastBN.

Machine Learning (ML) is changing DBs as many DB components are being replaced by ML models. One open problem in this setting is how to update such ML models in the presence of data updates. We start this investigation focusing on data insertions (dominating updates in analytical DBs). We study how to update neural network (NN) models when new data follows a different distribution (a.k.a. it is "out-of-distribution" -- OOD), rendering previously-trained NNs inaccurate. A requirement in our problem setting is that learned DB components should ensure high accuracy for tasks on old and new data (e.g., for approximate query processing (AQP), cardinality estimation (CE), synthetic data generation (DG), etc.). This paper proposes a novel updatability framework (DDUp). DDUp can provide updatability for different learned DB system components, even based on different NNs, without the high costs to retrain the NNs from scratch. DDUp entails two components: First, a novel, efficient, and principled statistical-testing approach to detect OOD data. Second, a novel model updating approach, grounded on the principles of transfer learning with knowledge distillation, to update learned models efficiently, while still ensuring high accuracy. We develop and showcase DDUp's applicability for three different learned DB components, AQP, CE, and DG, each employing a different type of NN. Detailed experimental evaluation using real and benchmark datasets for AQP, CE, and DG detail DDUp's performance advantages.

Identifying statistical regularities in solutions to some tasks in multi-task reinforcement learning can accelerate the learning of new tasks. Skill learning offers one way of identifying these regularities by decomposing pre-collected experiences into a sequence of skills. A popular approach to skill learning is maximizing the likelihood of the pre-collected experience with latent variable models, where the latent variables represent the skills. However, there are often many solutions that maximize the likelihood equally well, including degenerate solutions. To address this underspecification, we propose a new objective that combines the maximum likelihood objective with a penalty on the description length of the skills. This penalty incentivizes the skills to maximally extract common structures from the experiences. Empirically, our objective learns skills that solve downstream tasks in fewer samples compared to skills learned from only maximizing likelihood. Further, while most prior works in the offline multi-task setting focus on tasks with low-dimensional observations, our objective can scale to challenging tasks with high-dimensional image observations.

Controlling the generative model to adapt a new domain with limited samples is a difficult challenge and it is receiving increasing attention. Recently, methods based on meta-learning have shown promising results for few-shot domain adaptation. However, meta-learning-based methods usually suffer from the problem of overfitting, which results in a lack of diversity in the generated texts. To avoid this problem, in this study, a novel framework based on reinforcement learning (RL) is proposed. In this framework, to increase the sample utilization of RL and decrease its sample requirement, maximum likelihood estimation learning is incorporated into the RL process. When there are only a few in-domain samples available, experimental results on five target domains in two few-shot configurations show that this framework performs better than baselines.

In this paper, a hyperparameter tuning based Bayesian optimization of digital twins is carried out to diagnose various faults in grid connected inverters. As fault detection and diagnosis require very high precision, we channelize our efforts towards an online optimization of the digital twins, which, in turn, allows a flexible implementation with limited amount of data. As a result, the proposed framework not only becomes a practical solution for model versioning and deployment of digital twins design with limited data, but also allows integration of deep learning tools to improve the hyperparameter tuning capabilities. For classification performance assessment, we consider different fault cases in virtual synchronous generator (VSG) controlled grid-forming converters and demonstrate the efficacy of our approach. Our research outcomes reveal the increased accuracy and fidelity levels achieved by our digital twin design, overcoming the shortcomings of traditional hyperparameter tuning methods.

Universal Approximation Theorems establish the density of various classes of neural network function approximators in $C(K, \mathbb{R}^m)$, where $K \subset \mathbb{R}^n$ is compact. In this paper, we aim to extend these guarantees by establishing conditions on learning tasks that guarantee their continuity. We consider learning tasks given by conditional expectations $x \mapsto \mathrm{E}\left[Y \mid X = x\right]$, where the learning target $Y = f \circ L$ is a potentially pathological transformation of some underlying data-generating process $L$. Under a factorization $L = T \circ W$ for the data-generating process where $T$ is thought of as a deterministic map acting on some random input $W$, we establish conditions (that might be easily verified using knowledge of $T$ alone) that guarantee the continuity of practically \textit{any} derived learning task $x \mapsto \mathrm{E}\left[f \circ L \mid X = x\right]$. We motivate the realism of our conditions using the example of randomized stable matching, thus providing a theoretical justification for the continuity of real-world learning tasks.