Despite recent advances in rank aggregation and mixture learning, there has been a limited amount of success for learning a mixture model for ranking data. Motivated by the problem of learning a mixture of ranking models from pair-wise comparisons, we consider mixture learning from partial observations. The generic approaches for mixture learning do not generalize to this setting. Matrix estimation, however, provides a way to recover a structured underlying matrix from its partial, noisy observations. We utilize matrix estimation as a pre-processing step to extend the mixture learning problem to allow for partial observations. Instantiating our matrix estimation subroutine with singular value thresholding, we provide a bound on the estimation error with respect to $\|\cdot\|_{2,\infty}$-norm. In particular, we show that if $p$ (the fraction of observed entries) scales as $\tilde{\Omega}((\frac{r}{d})^{\frac{1}{3}})$, then the normalized $\|\cdot\|_{2,\infty}$ error vanishes to $0$ as long as the underlying $N \times d$ ($N\geq d$) matrix is rank $r$; this holds true even if the noise is correlated across columns. As an application, we argue if $\Gamma p=\tilde{\Omega}(\sqrt{r})$, then the mixture components can be correctly identified with $N=poly(d)$ samples; $\Gamma$ is the minimum gap between the mixture means. Further, we argue a large class of popular ranking models (e.g., Mallow, Multinomial Logit (MNL) Model) satisfy the sub-gaussian property when viewed through a pairwise embedding lens. Hence, our method provides a sufficient condition for efficiently recovering the mixture components for an important class of models. For example, mixtures of $r$ components can be clustered correctly using $\tilde{O}(rn^4)$ pair-wise comparisons when the components are well-separated and distributed as per either a Mallows, MNL, or any Random Utility Model over $n$ items.

Bagging, a powerful ensemble method from machine learning, improves the performance of unstable predictors. Although the power of Bagging has been shown mostly in classification problems, we demonstrate the success of employing Bagging in sparse regression over the baseline method (L1 minimization). The framework employs the generalized version of the original Bagging with various bootstrap ratios. The performance limits associated with different choices of bootstrap sampling ratio L/m and number of estimates K is analyzed theoretically. Simulation shows that the proposed method yields state-of-the-art recovery performance, outperforming L1 minimization and Bolasso in the challenging case of low levels of measurements. A lower L/m ratio (60% - 90%) leads to better performance, especially with a small number of measurements. With the reduced sampling rate, SNR improves over the original Bagging by up to 24%. With a properly chosen sampling ratio, a reasonably small number of estimates K = 30 gives satisfying result, even though increasing K is discovered to always improve or at least maintain the performance.

2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important non parametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to be nearly minimax rate optimal for the class of functions with bounded variation. In this paper, we complement these worst case guarantees by investigating the adaptivity of the TVD estimator to functions which are piecewise constant on axis aligned rectangles. We rigorously show that, when the truth is piecewise constant, the ideally tuned TVD estimator performs better than in the worst case. We also study the issue of choosing the tuning parameter. In particular, we propose a fully data driven version of the TVD estimator which enjoys similar worst case risk guarantees as the ideally tuned TVD estimator.

The more statistical techniques a Data Scientist has mastered, the better the results can be. In this blog article, we want to introduce you to ten common techniques that should not be missing in the repertoire of a data scientist. In statistics, linear regression is a linear approach to modeling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables). The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression.

In the present paper, a method of defining the industrial process parameters for a new product using machine learning algorithms will be presented. The study will describe how to go from the product characteristics till the prediction of the suitable machine parameters to produce a good quality of this product, and this is based on an historical training dataset of similar products with their respective process parameters. In the first part of our study, we will focus on the ultrasonic welding process definition, welding parameters and on how it operate. While in second part, we present the design and implementation of the prediction models such multiple linear regression, support vector regression, and we compare them to an artificial neural networks algorithm. In the following part, we present a new application of Convolutional Neural Networks (CNN) to the industrial process parameters prediction. In addition, we will propose the generalization approach of our CNN to any prediction problem of industrial process parameters. Finally the results of the four methods will be interpreted and discussed.

Accurate classification of seizure types plays a crucial role in the treatment and disease management of epileptic patients. Epileptic seizure type not only impacts on the choice of drugs but also on the range of activities a patient can safely engage in. With recent advances being made towards artificial intelligence enabled automatic seizure detection, the next frontier is the automatic classification of seizure types. On that note, in this paper, we undertake the first study to explore the application of machine learning algorithms for multi-class seizure type classification. We used the recently released TUH EEG Seizure Corpus and conducted a thorough search space exploration to evaluate the performance of a combination of various pre-processing techniques, machine learning algorithms, and corresponding hyperparameters on this task. We show that our algorithms can reach a weighted F1 score of up to 0.907 thereby setting the first benchmark for scalp EEG based multi-class seizure type classification.

Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known as experimental design, that is, how to select the input settings where the computer simulator is run and the corresponding response is collected. Extra care should be taken in the selection process because computer simulators can be computationally expensive to run. The selection shall acknowledge and achieve the goal of the analysis. This article focuses on the goal of producing more accurate prediction which is important for risk assessment and decision making. We propose two new methods of design approaches that sequentially select input settings to achieve this goal. The approaches make novel applications of simultaneous and sequential contour estimations. Numerical examples are employed to demonstrate the effectiveness of the proposed approaches.

While optimization methodology has provided much of the underlying algorithmic machinery that has driven the theory and practice of machine learning in recent years, sampling-based methodology, in particular Markov chain Monte Carlo (MCMC), remains of critical importance, given its role in linking algorithms to statistical inference and, in particular, its ability to provide notions of confidence that are lacking in optimization-based methodology. However, the classical theory of MCMC is largely asymptotic and the theory has not developed as rapidly in recent years as the theory of optimization. Recently, however, a literature has emerged that derives nonasymptotic rates for MCMC algorithms [see, e.g., 9, 12, 10, 8, 6, 14, 21, 22, 2, 5]. This work has explicitly aimed at making use of ideas from optimization; in particular, whereas the classical literature on MCMC focused on reversible Markov chains, the recent literature has focused on nonreversible stochastic processes that are built on gradients [see, e.g., 18, 20, 3, 1]. In particular, the gradient-based Langevin algorithm [33, 32, 13] has been shown to be a form of gradient descent on the space of probabilities [see, e.g., 36]. What has not yet emerged is an analog of acceleration. Recall that the notion of acceleration has played a key role in gradient-based optimization methods [26]. In particular, the Nesterov accelerated gradient descent (AGD) method, an instance of the general family of "momentum methods," provably achieves faster convergence rate than gradient descent (GD) in a variety of settings [25]. Moreover, it achieves the optimal convergence rate under an oracle model of optimization complexity in the convex setting [24].

Estimating what would be an individual's potential response to varying levels of exposure to a treatment is of high practical relevance for several important fields, such as healthcare, economics and public policy. However, existing methods for learning to estimate such counterfactual outcomes from observational data are either focused on estimating average dose-response curves, limited to settings in which treatments do not have an associated dosage parameter, or both. Here, we present a novel machine-learning framework towards learning counterfactual representations for estimating individual dose-response curves for any number of treatment options with continuous dosage parameters. Building on the established potential outcomes framework, we introduce new performance metrics, model selection criteria, model architectures, and open benchmarks for estimating individual dose-response curves. Our experiments show that the methods developed in this work set a new state-of-the-art in estimating individual dose-response curves.

A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the least-squares parameter estimates. The optimal design is achieved by using the available (experimental) degrees of freedom such that more informative measurements are obtained. Unlike the commonly used approaches, which base the OED procedure upon the linearized CRs, we explore a path where we explicitly consider the exact CRs in the OED framework. We use a methodology for a finite parametrization of the exact CRs within the OED problem and we introduce a novel approximation technique of the exact CRs using inner-and outer-approximating ellipsoids as a computationally less demanding alternative. The employed techniques give the OED problem as a finite-dimensional mathematical program of bilevel nature. We use two small-scale illustrative case studies to study various OED criteria and compare the resulting optimal designs with the commonly used linearization-based approach. We also assess the performance of two simple heuristic numerical schemes for bilevel optimization within the studied problems. Introduction At present, advanced industrial engineering and management strive for resource-and energy-efficient design and operation of systems, plants, and processes. Here a use of the model-based techniques is a leading paradigm. The employed models, whether mechanistic or data-based, include a finite number of parameters, whose values are related to the particular natural and system-wide phenomena and are thus commonly only known to belong to some interval or unknown completely.