Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and noise can make this single estimate inaccurate or misleading. While deep networks such as conditional normalizing flows can be used to sample posteriors in inverse problems, they often yield low-quality samples and uncertainty estimates. In this paper, we propose U-Flow, a Bayesian U-Net based on conditional normalizing flows, which generates high-quality posterior samples and estimates physically-meaningful uncertainty. We show that the proposed model significantly outperforms the recent normalizing flows in terms of posterior sample quality while having comparable performance with the U-Net in point estimation.

Emerging applications such as Deep Learning are often data-driven, thus traditional approaches based on auto-tuners are not performance effective across the wide range of inputs used in practice. In the present paper, we start an investigation of predictive models based on machine learning techniques in order to optimize Convolution Neural Networks (CNNs). As a use-case, we focus on the ARM Compute Library which provides three different implementations of the convolution operator at different numeric precision. Starting from a collation of benchmarks, we build and validate models learned by Decision Tree and naive Bayesian classifier. Preliminary experiments on Midgard-based ARM Mali GPU show that our predictive model outperforms all the convolution operators manually selected by the library.

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.

The primary aim of this research was to find a model that best predicts which fallen angel bonds would either potentially rise up back to investment grade bonds and which ones would fall into bankruptcy. To implement the solution, we thought that the ideal method would be to create an optimal machine learning model that could predict bankruptcies. Among the many machine learning models out there we decided to pick four classification methods: logistic regression, KNN, SVM, and NN. We also utilized an automated methods of Google Cloud's machine learning. The results of our model comparisons showed that the models did not predict bankruptcies very well on the original data set with the exception of Google Cloud's machine learning having a high precision score. However, our over-sampled and feature selection data set did perform very well. This could likely be due to the model being over-fitted to match the narrative of the over-sampled data (as in, it does not accurately predict data outside of this data set quite well). Therefore, we were not able to create a model that we are confident that would predict bankruptcies. However, we were able to find value out of this project in two key ways. The first is that Google Cloud's machine learning model in every metric and in every data set either outperformed or performed on par with the other models. The second is that we found that utilizing feature selection did not reduce predictive power that much. This means that we can reduce the amount of data to collect for future experimentation regarding predicting bankruptcies.

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.

Whether based on models, training data or a combination, classifiers place (possibly complex) input data into one of a relatively small number of output categories. In this paper, we study the structure of the boundary--those points for which a neighbor is classified differently--in the context of an input space that is a graph, so that there is a concept of neighboring inputs, The scientific setting is a model-based naive Bayes classifier for DNA reads produced by Next Generation Sequencers. We show that the boundary is both large and complicated in structure. We create a new measure of uncertainty, called Neighbor Similarity, that compares the result for a point to the distribution of results for its neighbors. This measure not only tracks two inherent uncertainty measures for the Bayes classifier, but also can be implemented, at a computational cost, for classifiers without inherent measures of uncertainty.

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.