Markov chain Monte Carlo (MCMC) algorithms offer various strategies for sampling; the Hamiltonian Monte Carlo (HMC) family of samplers are MCMC algorithms which often exhibit improved mixing properties. The recently introduced magnetic HMC, a generalization of HMC motivated by the physics of particles influenced by magnetic field forces, has been demonstrated to improve the performance of HMC. In many applications, one wishes to sample from a distribution restricted to a constrained set, often manifested as an embedded manifold (for example, the surface of a sphere). We introduce magnetic manifold HMC, an HMC algorithm on embedded manifolds motivated by the physics of particles constrained to a manifold and moving under magnetic field forces. We discuss the theoretical properties of magnetic Hamiltonian dynamics on manifolds, and introduce a reversible and symplectic integrator for the HMC updates. We demonstrate that magnetic manifold HMC produces favorable sampling behaviors relative to the canonical variant of manifold-constrained HMC.

We introduce Hyperbolic Prototype Learning, a type of supervised learning, where class labels are represented by ideal points (points at infinity) in hyperbolic space. Learning is achieved by minimizing the 'penalized Busemann loss', a new loss function based on the Busemann function of hyperbolic geometry. We discuss several theoretical features of this setup. In particular, Hyperbolic Prototype Learning becomes equivalent to logistic regression in the one-dimensional case.

Selecting relevant features in a time series model is a longstanding open problem in both statistics and econometrics. Traditional feature selection approaches, such as those proposed by Box and Jenkins (1994) rely on heuristic methods, such as visual inspection of diagnostic plots. Alternatively, popular data-driven approaches select features based upon the minimization of information criterion, such as Akaike's Information Criterion (AIC, Akaike 1974) or Bayesian Information Criterion (BIC, Schwarz et al. 1978) over a subset of potential models. Typically, because the space of all possible models is extremely large, such methods require imposing substantial restrictions on the feature space. More recent approaches have extended the lasso (Tibshirani, 1996) to a time dependent setting. The lasso has advantages over conventional methods in that it shrinks least squares estimates toward zero in addition to performing feature selection. It also allows for estimation under scenarios in which there are more potential features than observations.

In this paper, we aim to address the problem of solving a non-convex optimization problem over an intersection of multiple variable sets. This kind of problems is typically solved by using an alternating minimization (AM) strategy which splits the overall problem into a set of sub-problems corresponding to each variable, and then iteratively performs minimization over each sub-problem using a fixed updating rule. However, due to the intrinsic non-convexity of the overall problem, the optimization can usually be trapped into bad local minimum even when each sub-problem can be globally optimized at each iteration. To tackle this problem, we propose a meta-learning based Global Scope Optimization (GSO) method. It adaptively generates optimizers for sub-problems via meta-learners and constantly updates these meta-learners with respect to the global loss information of the overall problem. Therefore, the sub-problems are optimized with the objective of minimizing the global loss specifically. We evaluate the proposed model on a number of simulations, including solving bi-linear inverse problems: matrix completion, and non-linear problems: Gaussian mixture models. The experimental results show that our proposed approach outperforms AM-based methods in standard settings, and is able to achieve effective optimization in some challenging cases while other methods would typically fail.

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. We assess the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.

We study the transfer learning process between two linear regression problems. An important and timely special case is when the regressors are overparameterized and perfectly interpolate their training data. We examine a parameter transfer mechanism whereby a subset of the parameters of the target task solution are constrained to the values learned for a related source task. We analytically characterize the generalization error of the target task in terms of the salient factors in the transfer learning architecture, i.e., the number of examples available, the number of (free) parameters in each of the tasks, the number of parameters transferred from the source to target task, and the correlation between the two tasks. Our non-asymptotic analysis shows that the generalization error of the target task follows a two-dimensional double descent trend (with respect to the number of free parameters in each of the tasks) that is controlled by the transfer learning factors. Our analysis points to specific cases where the transfer of parameters is beneficial.

The work reported here addresses the capacity of psychophysiological sensors and measures using Electroencephalogram (EEG) and Galvanic Skin Response (GSR) to detect levels of trust for humans using AI-supported Human-Machine Interaction (HMI). Improvements to the analysis of EEG and GSR data may create models that perform as well, or better than, traditional tools. A challenge to analyzing the EEG and GSR data is the large amount of training data required due to a large number of variables in the measurements. Researchers have routinely used standard machine-learning classifiers like artificial neural networks (ANN), support vector machines (SVM), and K-nearest neighbors (KNN). Traditionally, these have provided few insights into which features of the EEG and GSR data facilitate the more and least accurate predictions - thus making it harder to improve the HMI and human-machine trust relationship. A key ingredient to applying trust-sensor research results to practical situations and monitoring trust in work environments is the understanding of which key features are contributing to trust and then reducing the amount of data needed for practical applications. We used the Local Interpretable Model-agnostic Explanations (LIME) model as a process to reduce the volume of data required to monitor and enhance trust in HMI systems - a technology that could be valuable for governmental and public sector applications. Explainable AI can make HMI systems transparent and promote trust. From customer service in government agencies and community-level non-profit public service organizations to national military and cybersecurity institutions, many public sector organizations are increasingly concerned to have effective and ethical HMI with services that are trustworthy, unbiased, and free of unintended negative consequences.

Traditional recommender systems encounter several challenges such as data sparsity and unexplained recommendation. To address these challenges, many works propose to exploit semantic information from review data. However, these methods have two major limitations in terms of the way to model textual features and capture textual interaction. For textual modeling, they simply concatenate all the reviews of a user/item into a single review. However, feature extraction at word/phrase level can violate the meaning of the original reviews. As for textual interaction, they defer the interactions to the prediction layer, making them fail to capture complex correlations between users and items. To address those limitations, we propose a novel Hierarchical Text Interaction model(HTI) for rating prediction. In HTI, we propose to model low-level word semantics and high-level review representations hierarchically. The hierarchy allows us to exploit textual features at different granularities. To further capture complex user-item interactions, we propose to exploit semantic correlations between each user-item pair at different hierarchies. At word level, we propose an attention mechanism specialized to each user-item pair, and capture the important words for representing each review. At review level, we mutually propagate textual features between the user and item, and capture the informative reviews. The aggregated review representations are integrated into a collaborative filtering framework for rating prediction. Experiments on five real-world datasets demonstrate that HTI outperforms state-of-the-art models by a large margin. Further case studies provide a deep insight into HTI's ability to capture semantic correlations at different levels of granularities for rating prediction.

Extracting entity pairs along with relation types from unstructured texts is a fundamental subtask of information extraction. Most existing joint models rely on fine-grained labeling scheme or focus on shared embedding parameters. These methods directly model the joint probability of multi-labeled triplets, which suffer from extracting redundant triplets with all relation types. However, each sentence may contain very few relation types. In this paper, we first model the final triplet extraction result as a three-order tensor of word-to-word pairs enriched with each relation type. And in order to obtain the sentence contained relations, we introduce an independent but joint training relation classification module. The tensor decomposition strategy is finally utilized to decompose the triplet tensor with predicted relational components which omits the calculations for unpredicted relation types. According to effective decomposition methods, we propose the Tensor Decomposition based Relation Extraction (TDRE) approach which is able to extract overlapping triplets and avoid detecting unnecessary entity pairs. Experiments on benchmark datasets NYT, CoNLL04 and ADE datasets demonstrate that the proposed method outperforms existing strong baselines.

Free Coupon Discount - Machine Learning Regression Masterclass in Python, Build 8 Practical Projects and Master Machine Learning Regression Techniques Using Python, Scikit Learn and Keras Created by Dr. Ryan Ahmed, Ph.D., MBA, Kirill Eremenko, Hadelin de Ponteves, SuperDataScience Team, Mitchell Bouchard Students also bought Unsupervised Deep Learning in Python Deep Learning Prerequisites: Linear Regression in Python Neural Networks in Python from Scratch: Complete guide Artificial Intelligence: Optimization Algorithms in Python Machine Learning Practical: 6 Real-World Applications Preview this Udemy Course GET COUPON CODE Description Artificial Intelligence (AI) revolution is here! The technology is progressing at a massive scale and is being widely adopted in the Healthcare, defense, banking, gaming, transportation and robotics industries. Machine Learning is a subfield of Artificial Intelligence that enables machines to improve at a given task with experience. Machine Learning is an extremely hot topic; the demand for experienced machine learning engineers and data scientists has been steadily growing in the past 5 years. According to a report released by Research and Markets, the global AI and machine learning technology sectors are expected to grow from $1.4B to $8.8B by 2022 and it is predicted that AI tech sector will create around 2.3 million jobs by 2020.