In this paper, we propose a new optimization algorithm for sparse logistic regression based on a stochastic version of the Douglas-Rachford splitting method. Our algorithm sweeps the training set by randomly selecting a mini-batch of data at each iteration, and it allows us to update the variables in a block coordinate manner. Our approach leverages the proximity operator of the logistic loss, which is expressed with the generalized Lambert W function. Experiments carried out on standard datasets demonstrate the efficiency of our approach w.r.t. stochastic gradient-like methods.

We propose a new variational Bayes method for estimating high-dimensional copulas with discrete, or discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is substantially faster than previous likelihood-based approaches. We use it to estimate drawable vine copulas for univariate and multivariate Markov ordinal and mixed time series. These have dimension $rT$, where $T$ is the number of observations and $r$ is the number of series, and are difficult to estimate using previous methods. The vine pair-copulas are carefully selected to allow for heteroskedasticity, which is a common feature of ordinal time series data. When combined with flexible margins, the resulting time series models also allow for other common features of ordinal data, such as zero inflation, multiple modes and under- or over-dispersion. Using data on homicides in New South Wales, and also U.S bankruptcies, we illustrate both the flexibility of the time series copula models, and the efficacy of the variational Bayes estimator for copulas of up to 792 dimensions and 60 parameters. This far exceeds the size and complexity of copula models for discrete data that can be estimated using previous methods.

Significant success has been realized recently on applying machine learning to real-world applications. There have also been corresponding concerns on the privacy of training data, which relates to data security and confidentiality issues. Differential privacy provides a principled and rigorous privacy guarantee on machine learning models. While it is common to design a model satisfying a required differential-privacy property by injecting noise, it is generally hard to balance the trade-off between privacy and utility. We show that stochastic gradient Markov chain Monte Carlo (SG-MCMC) -- a class of scalable Bayesian posterior sampling algorithms proposed recently -- satisfies strong differential privacy with carefully chosen step sizes. We develop theory on the performance of the proposed differentially-private SG-MCMC method. We conduct experiments to support our analysis and show that a standard SG-MCMC sampler without any modification (under a default setting) can reach state-of-the-art performance in terms of both privacy and utility on Bayesian learning.

Get your team access to Udemy's top 2,000 courses anytime, anywhere. This course has two parts. Part one refers to Dummy Variable Regression and part two refers to conjoint analysis. Let me give you details of what you are going to get in each part. How to know, what kind of situation you have.

The answer to the question "What machine learning algorithm should I use?" is always "It depends." It depends on the size, quality, and nature of the data. It depends on what you want to do with the answer. It depends on how the math of the algorithm was translated into instructions for the computer you are using. And it depends on how much time you have. Even the most experienced data scientists can't tell which algorithm will perform best before trying them.

It explores main concepts from basic to expert level which can help you achieve better grades, develop your academic career, apply your knowledge at work or do your research as experienced investor. Learning machine trading analysis is indispensable for finance careers in areas such as computational finance research, computational finance development, and computational finance trading mainly within investment banks and hedge funds. It is also essential for academic careers in computational finance. And it is necessary for experienced investors computational finance trading research and development. But as learning curve can become steep as complexity grows, this course helps by leading you step by step using S&P 500 Index ETF prices historical data for back-testing to achieve greater effectiveness.

In my previous post I outlined how machine learning works by demonstrating the central role that cost functions and gradient descent play in the learning process. This post builds on these concepts by exploring how neural networks and deep learning work. This post is light on explanation and heavy on code. The reason for this is that I cannot think of any way to elucidate the internal workings of a neural network more clearly that the incredible videos put together by three blue one brown -- see the full playlist here. These videos show how neural networks can be fed raw data -- such as images of digits -- and can output labels for these images with amazing accuracy.

So, what are Markov chain Monte Carlo (MCMC) methods? In this article, I will explain that short answer, without any math. A parameter of interest is just some number that summarizes a phenomenon we're interested in. In general we use statistics to estimate parameters. For example, if we want to learn about the height of human adults, our parameter of interest might be average height in in inches.

R is a data analysis tool, graphical environment, and programming language. Without any prior experience in programming or statistical software, this video tutorial will help you quickly become a knowledgeable user of R. Now is the time to take control of your data and start producing superior statistical analysis with R. In this video tutorial, you will start with a quick refresher on programming in R. You will learn to set up your R development environment, as well as work on a few simple R programs. After that you will dive right into working with different types of data structures in R, such as vectors, lists, matrices, etc. You will explore how to import and export data for your data analysis project, and also connect to databases such as PostgreSQL.

This course is about artificial neural networks. Artificial intelligence and machine learning are getting more and more popular nowadays. In the beginning, other techniques such as Support Vector Machines outperformed neural networks, but in the 21th century neural networks again gain popularity. In spite of the slow training procedure, neural networks can be very powerful. In the first part of the course you will learn about the theoretical background of neural networks, later you will learn how to implement them.