We consider the problem of the estimation of a high-dimensional probability distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated with a dimension partition tree. The distribution is assumed to admit a density with respect to a product measure, possibly discrete for handling the case of discrete random variables. After discussing the representation of classical model classes in tree-based tensor formats, we present learning algorithms based on empirical risk minimization using a $L^2$ contrast. These algorithms exploit the multilinear parametrization of the formats to recast the nonlinear minimization problem into a sequence of empirical risk minimization problems with linear models. A suitable parametrization of the tensor in tree-based tensor format allows to obtain a linear model with orthogonal bases, so that each problem admits an explicit expression of the solution and cross-validation risk estimates. These estimations of the risk enable the model selection, for instance when exploiting sparsity in the coefficients of the representation. A strategy for the adaptation of the tensor format (dimension tree and tree-based ranks) is provided, which allows to discover and exploit some specific structures of high-dimensional probability distributions such as independence or conditional independence. We illustrate the performances of the proposed algorithms for the approximation of classical probabilistic models (such as Gaussian distribution, graphical models, Markov chain).

This paper formulates the problem of building a context-aware predictive model based on user diverse behavioral activities with smartphones. In the area of machine learning and data science, a tree-like model as that of decision tree is considered as one of the most popular classification techniques, which can be used to build a data-driven predictive model. The traditional decision tree model typically creates a number of leaf nodes as decision nodes that represent context-specific rigid decisions, and consequently may cause overfitting problem in behavior modeling. However, in many practical scenarios within the context-aware environment, the generalized outcomes could play an important role to effectively capture user behavior. In this paper, we propose a behavioral decision tree, "BehavDT" context-aware model that takes into account user behavior-oriented generalization according to individual preference level. The BehavDT model outputs not only the generalized decisions but also the context-specific decisions in relevant exceptional cases. The effectiveness of our BehavDT model is studied by conducting experiments on individual user real smartphone datasets. Our experimental results show that the proposed BehavDT context-aware model is more effective when compared with the traditional machine learning approaches, in predicting user diverse behaviors considering multi-dimensional contexts.

Investigation of human brain states through electroencephalograph (EEG) signals is a crucial step in human-machine communications. However, classifying and analyzing EEG signals are challenging due to their noisy, nonlinear and nonstationary nature. Current methodologies for analyzing these signals often fall short because they have several regularity assumptions baked in. This work provides an effective, flexible and noise-resilient scheme to analyze EEG by extracting pertinent information while abiding by the 3N (noisy, nonlinear and nonstationary) nature of data. We implement a topological tool, namely persistent homology, that tracks the evolution of topological features over time intervals and incorporates individual's expectations as prior knowledge by means of a Bayesian framework to compute posterior distributions. Relying on these posterior distributions, we apply Bayes factor classification to noisy EEG measurements. The performance of this Bayesian classification scheme is then compared with other existing methods for EEG signals.

W e introduce Hyper-Conditioned Neural Autoregres-sive Flow (HCNAF); a powerful universal distribution ap-proximator designed to model arbitrarily complex conditional probability density functions. HCNAF consists of a neural-net based conditional autoregressive flow (AF) and a hyper-network that can take large conditions in non-autoregressive fashion and outputs the network parameters of the AF . Like other flow models, HCNAF performs exact likelihood inference. W e demonstrate the effectiveness and attributes of HCNAF, including its generalization capability over unseen conditions and show that HCNAF outperforms recent flow models in a conditional density estimation task for MNIST. W e also show that HCNAF scales up to complex high-dimensional prediction problems of the magnitude of self-driving and that HCNAF yields a state-of-the-art performance in a public self-driving dataset.

Online behaviors of consumers and marketers generate massive marketing data, which ever more sophisticated models attempt to turn into insights and aid decisions by marketers. Yet, in making decisions human managers bring to bear marketing knowledge which reside outside of data and models. Thus, it behooves creation of an automated marketing knowledge base that can interact with data and models. Currently, marketing knowledge is dispersed in large corpora, but no definitive knowledge base for marketing exists. Out of the two broad aspects of marketing knowledge - representation and reasoning - this treatise focuses on the former. Specifically, we focus on creation of marketing knowledge graph from corpora, which requires identification of entities and relations. The relation identification task is particularly challenging in marketing, because of the non-factoid nature of much marketing knowledge, and the difficulty of forming rules that govern relations. Specifically, we define a set of relations to capture marketing knowledge, propose a pipeline for creating the knowledge graph from text and propose a rule-guided semi-supervised relation prediction algorithm to extract relations between marketing entities from sentences.

This article discusses how the language of causality can shed new light on the major challenges in machine learning for medical imaging: 1) data scarcity, which is the limited availability of high-quality annotations, and 2) data mismatch, whereby a trained algorithm may fail to generalize in clinical practice. Looking at these challenges through the lens of causality allows decisions about data collection, annotation procedures, and learning strategies to be made (and scrutinized) more transparently. We discuss how causal relationships between images and annotations can not only have profound effects on the performance of predictive models, but may even dictate which learning strategies should be considered in the first place. For example, we conclude that semi-supervision may be unsuitable for image segmentation---one of the possibly surprising insights from our causal analysis, which is illustrated with representative real-world examples of computer-aided diagnosis (skin lesion classification in dermatology) and radiotherapy (automated contouring of tumours). We highlight that being aware of and accounting for the causal relationships in medical imaging data is important for the safe development of machine learning and essential for regulation and responsible reporting. To facilitate this we provide step-by-step recommendations for future studies.

In supervised learning, algorithms learn from labeled data. After understanding the data, the algorithm determines which label should be given to new data by associating patterns to the unlabeled new data. Supervised learning can be divided into two categories: classification and regression. Some examples of classification include spam detection, churn prediction, sentiment analysis, dog breed detection and so on. Some examples of regression include house price prediction, stock price prediction, height-weight prediction and so on.

Full Wave Inversion (FWI) imaging scheme has many applications in engineering, geoscience and medical sciences. In this paper, a surrogate deep learning FWI approach is presented to quantify properties of materials using stress waves. Such inverse problems, in general, are ill-posed and nonconvex, especially in cases where the solutions exhibit shocks, heterogeneity, discontinuities, or large gradients. The proposed approach is proven efficient to obtain global minima responses in these cases. This approach is trained based on random sampled set of material properties and sampled trials around local minima, therefore, it requires a forward simulation can handle high heterogeneity, discontinuities and large gradients. High resolution Kurganov-Tadmor (KT) central finite volume method is used as forward wave propagation operator. Using the proposed framework, material properties of 2D media are quantified for several different situations. The results demonstrate the feasibility of the proposed method for estimating mechanical properties of materials with high accuracy using deep learning approaches.

Estimating arbitrary quantities of interest (QoIs) that are non-linear operators of complex, expensive-to-evaluate, black-box functions is a challenging problem due to missing domain knowledge and finite budgets. Bayesian optimal design of experiments (BODE) is a family of methods that identify an optimal design of experiments (DOE) under different contexts, using only in a limited number of function evaluations. Under BODE methods, sequential design of experiments (SDOE) accomplishes this task by selecting an optimal sequence of experiments while using data-driven probabilistic surrogate models instead of the expensive black-box function. Probabilistic predictions from the surrogate model are used to define an information acquisition function (IAF) which quantifies the marginal value contributed or the expected information gained by a hypothetical experiment. The next experiment is selected by maximizing the IAF. A generally applicable IAF is the expected information gain (EIG) about a QoI as captured by the expectation of the Kullback-Leibler divergence between the predictive distribution of the QoI after doing a hypothetical experiment and the current predictive distribution about the same QoI. We model the underlying information source as a fully-Bayesian, non-stationary Gaussian process (FBNSGP), and derive an approximation of the information gain of a hypothetical experiment about an arbitrary QoI conditional on the hyper-parameters The EIG about the same QoI is estimated by sample averages to integrate over the posterior of the hyper-parameters and the potential experimental outcomes. We demonstrate the performance of our method in four numerical examples and a practical engineering problem of steel wire manufacturing. The method is compared to two classic SDOE methods: random sampling and uncertainty sampling.

Conditional mean embeddings (CME) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert spaces (RKHSs) by providing a linear-algebraic relation for the kernel mean embeddings of the respective probability distributions. Both centered and uncentered covariance operators have been used to define CMEs in the existing literature. In this paper, we develop a mathematically rigorous theory for both variants, discuss the merits and problems of either, and significantly weaken the conditions for applicability of CMEs. In the course of this, we demonstrate a beautiful connection to Gaussian conditioning in Hilbert spaces.