Portfolio optimization emerged with the seminal paper of Markowitz (1952). The original mean-variance framework is appealing because it is very efficient from a computational point of view. However, it also has one well-established failing since it can lead to portfolios that are not optimal from a financial point of view. Nevertheless, very few models have succeeded in providing a real alternative solution to the Markowitz model. The main reason lies in the fact that most academic portfolio optimization models are intractable in real life although they present solid theoretical properties. By intractable we mean that they can be implemented for an investment universe with a small number of assets using a lot of computational resources and skills, but they are unable to manage a universe with dozens or hundreds of assets. However, the emergence and the rapid development of robo-advisors means that we need to rethink portfolio optimization and go beyond the traditional mean-variance optimization approach. Another industry has faced similar issues concerning large-scale optimization problems. Machine learning has long been associated with linear and logistic regression models. Again, the reason was the inability of optimization algorithms to solve high-dimensional industrial problems. Nevertheless, the end of the 1990s marked an important turning point with the development and the rediscovery of several methods that have since produced impressive results. The goal of this paper is to show how portfolio allocation can benefit from the development of these large-scale optimization algorithms. Not all of these algorithms are useful in our case, but four of them are essential when solving complex portfolio optimization problems. These four algorithms are the coordinate descent, the alternating direction method of multipliers, the proximal gradient method and the Dykstra's algorithm.

Mixed effects (ME) models inform a vast array of problems in the physical and social sciences, and are pervasive in meta-analysis. We consider ME models where the random effects component is linear. We then develop an efficient approach for a broad problem class that allows nonlinear measurements, priors, and constraints, and finds robust estimates in all of these cases using trimming in the associated marginal likelihood. We illustrate the efficacy of the approach on a range of applications for meta-analysis of global health data. Constraints and priors are used to impose monotonicity, convexity and other characteristics on dose-response relationships, while nonlinear observations enable new epidemiological analyses in place of approximations. Robust extensions ensure that spurious studies do not drive our understanding of between-study heterogeneity. The software accompanying this paper is disseminated as an open-source Python package called limeTR.

Data visualization: In this section, you will learn how to create simple plots like scatter plot histogram bar, etc. Data manipulation: You will learn in detail about data manipulation. GUI Programming: This section is a combination of life instructor-led training and self-paced learning. Developing web Maps and representing information using plots: In this section, you will understand how to design Python applications. Computer vision using open CV and visualization using bokeh: You will also learn designing Python application in the section.

-- In cognitive psychology, automatic and self-reinforcing irrational thought patterns are known as cognitive distortions. Left unchecked, patients exhibiting these types of thoughts can become stuck in negative feedback loops of unhealthy thinking, leading to inaccurate perceptions of reality commonly associated with anxiety and depression. In this paper, we present a machine learning framework for the automatic detection and classification of 15 common cognitive distortions in two novel mental health free text datasets collected from both crowdsourcing and a real-world online therapy program. When differentiating between distorted and non-distorted passages, our model achieved a weighted F1 score of 0.88. For classifying distorted passages into one of 15 distortion categories, our model yielded weighted F1 scores of 0.68 in the larger crowdsourced dataset and 0.45 in the smaller online counseling dataset, both of which outperformed random baseline metrics by a large margin. For both tasks, we also identified the most discriminative words and phrases between classes to highlight common thematic elements for improving targeted and therapist-guided mental health treatment. Furthermore, we performed an exploratory analysis using unsupervised content-based clustering and topic modeling algorithms as first efforts towards a data-driven perspective on the thematic relationship between similar cognitive distortions traditionally deemed unique. Finally, we highlight the difficulties in applying mental health-based machine learning in a real-world setting and comment on the implications and benefits of our framework for improving automated delivery of therapeutic treatment in conjunction with traditional cognitive-behavioral therapy. CCORDING to the National Institute of Mental Health, anxiety disorders affect more than 18% of the U.S. adult population every year [1]. Additionally, the National Survey of Drug Use and Health reports that 6.7% of the U.S. adult population experienced at least one major depressive disorder episode in the past year [2]. This work was supported by NSF-IIP 1631871 from the National Science Foundation (NSF), Division of Industrial Innovation and Partnerships (IIP). Rashidi are with the University of Florida, Gainesville, FL 32611 USA (email: shickelb@ufl.edu; S. Benton is with T AO Connect, Inc., St. Petersburg, FL 33701 USA (email: sherry .benton@taoconnect.org).

Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence speed, adaptivity and structural awareness. However, distributional aspects of these new algorithms are poorly understood, especially for structured parameters. To develop statistical inference in this case, we propose a class of generalized regularized dual averaging (gRDA) algorithms with constant step size, which improves RDA (Xiao, 2010; Flammarion and Bach, 2017). Weak convergence of gRDA trajectories are studied, and as a consequence, for the first time in the literature, the asymptotic distributions for online l1 penalized problems become available. These general results apply to both convex and non-convex differentiable loss functions, and in particular, recover the existing regret bound for convex losses (Nemirovski et al., 2009). As important applications, statistical inferential theory on online sparse linear regression and online sparse principal component analysis are developed, and are supported by extensive numerical analysis. Interestingly, when gRDA is properly tuned, support recovery and central limiting distribution (with mean zero) hold simultaneously in the online setting, which is in contrast with the biased central limiting distribution of batch Lasso (Knight and Fu, 2000). Technical devices, including weak convergence of stochastic mirror descent, are developed as by-products with independent interest. Preliminary empirical analysis of modern image data shows that learning very sparse deep neural networks by gRDA does not necessarily sacrifice testing accuracy.

This first video in the logistic regression series introduces this powerful classification algorithm. The logistic regression algorithm is used when the dependent variable or target variable is categorical. Simple Logistic Regression and Multinomial Logistic Regression are explained. This second video in the logistic regression series compares logistic regression with linear regression in terms of their purpose, use cases, equations, error minimizations, and assumptions. This third video in the logistic regression series covers the four ways of preprocessing data before performing logistic regression: missing data handling, categorical data handling, splitting into train and test set, and feature scaling.

In this paper, we study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured model -- an actively studied topic in statistics and machine learning. In the noiseless case, we provide matching upper and lower bounds on sample complexity for the exact recovery of sparse vectors and for stable estimation of approximately sparse vectors, respectively. In the noisy case, we develop upper and matching minimax lower bounds for estimation error. We also consider the debiased sparse group Lasso and investigate its asymptotic property for the purpose of statistical inference. Finally, numerical studies are provided to support the theoretical results.

First, and arguably the most popular type of machine learning algorithm, is linear regression. Linear regression algorithms map simple correlations between two variables in a set of data. A set of inputs and their corresponding outputs are examined and quantified to show a relationship, including how a change in one variable affects the other. Linear regressions are plotted via a line on a graph. Linear regression's popularity is due to its simplicity: The algorithm is easily explainable, relatively transparent and requires little to no parameter tuning.

If you are predicting the label $y$ of a new object with $\hat y$, how confident are you that $y = \hat y$? Conformal prediction methods provide an elegant framework for answering such question by building a $100 (1 - \alpha)\%$ confidence region without assumptions on the distribution of the data. It is based on a refitting procedure that parses all the possibilities for $y$ to select the most likely ones. Although providing strong coverage guarantees, conformal set is impractical to compute exactly for many regression problems. We propose efficient algorithms to compute conformal prediction set using approximated solution of (convex) regularized empirical risk minimization. Our approaches rely on a new homotopy continuation technique for tracking the solution path w.r.t. sequential changes of the observations. We provide a detailed analysis quantifying its complexity.

A recently proposed SLOPE estimator (arXiv:1407.3824) has been shown to adaptively achieve the minimax $\ell_2$ estimation rate under high-dimensional sparse linear regression models (arXiv:1503.08393). Such minimax optimality holds in the regime where the sparsity level $k$, sample size $n$, and dimension $p$ satisfy $k/p \rightarrow 0$, $k\log p/n \rightarrow 0$. In this paper, we characterize the estimation error of SLOPE under the complementary regime where both $k$ and $n$ scale linearly with $p$, and provide new insights into the performance of SLOPE estimators. We first derive a concentration inequality for the finite sample mean square error (MSE) of SLOPE. The quantity that MSE concentrates around takes a complicated and implicit form. With delicate analysis of the quantity, we prove that among all SLOPE estimators, LASSO is optimal for estimating $k$-sparse parameter vectors that do not have tied non-zero components in the low noise scenario. On the other hand, in the large noise scenario, the family of SLOPE estimators are sub-optimal compared with bridge regression such as the Ridge estimator.