We describe an application of machine learning to the problem of predicting preterm birth. We conduct a secondary analysis on a clinical trial dataset collected by the National In- stitute of Child Health and Human Development (NICHD) while focusing our attention on predicting different classes of preterm birth. We compare three approaches for deriving predictive models: a support vector machine (SVM) approach with linear and non-linear kernels, logistic regression with different model selection along with a model based on decision rules prescribed by physician experts for prediction of preterm birth. Our approach highlights the pre-processing methods applied to handle the inherent dynamics, noise and gaps in the data and describe techniques used to handle skewed class distributions. Empirical experiments demonstrate significant improvement in predicting preterm birth compared to past work.

We describe GTApprox -- a new tool for medium-scale surrogate modeling in industrial design. Compared to existing software, GTApprox brings several innovations: a few novel approximation algorithms, several advanced methods of automated model selection, novel options in the form of hints. We demonstrate the efficiency of GTApprox on a large collection of test problems. In addition, we describe several applications of GTApprox to real engineering problems. Keywords: 1. Introduction approximation, surrogate model, surrogate-based optimization Approximation problems (also known as regression problems) arise quite often in industrial design, and solutions of such problems are conventionally referred to as surrogate models [1]. The most common application of surrogate modeling in engineering is in connection to engineering optimization [2]. Indeed, on the one hand, design optimization plays a central role in the industrial design process; on the other hand, a single optimization step typically requires the optimizer to create or refresh a model of the response function whose optimum is sought, to be able to come up with a reasonable next design candidate. The surrogate models used in optimization range from simple local linear regression employed in the basic gradient-based optimization [3] to complex global models employed in the so-called Surrogate-Based Optimization (SBO) [4]. Aside from optimization, surrogate modeling is used in dimension reduction [5, 6], sensitivity analysis [7-10], and for visualization of response functions. Preprint submitted to February 23, 2018 Mathematically, the approximation problem can generally be described as follows. A great variety of surrogate modeling methods exist, with different assumptions on the underlying response functions, data sets, and model structure [11].

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the conditional likelihood, only needing its evaluation as a black-box function. Using a mixture of Gaussians as the variational distribution, we show that the evidence lower bound and its gradients can be estimated efficiently using empirical expectations over univariate Gaussian distributions. Furthermore, the method is scalable to large datasets which is achieved by using an augmented prior via the inducing-variable approach underpinning most sparse GP approximations, along with parallel computation and stochastic optimization. We evaluate our method with experiments on small datasets, medium-scale datasets and a large dataset, showing its competitiveness under different likelihood models and sparsity levels. Moreover, we analyze learning in our model under batch and stochastic settings, and study the effect of optimizing the inducing inputs. Finally, in the large-scale experiment, we investigate the problem of predicting airline delays and show that our method is on par with the state-of-the-art hard-coded approach for scalable GP regression.

The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-$\ell_1$-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection and prediction properties, as well as minimax optimality. This paper introduces the Bayesian SLOPE procedure for linear regression. The classical SLOPE estimate is the posterior mode in the normal regression problem with an appropriate prior on the coefficients. The Bayesian SLOPE considers the full Bayesian model and has the advantage of offering credible sets and standard error estimates for the parameters. Moreover, the hierarchical Bayesian framework allows for full Bayesian and empirical Bayes treatment of the penalty coefficients; whereas it is not clear how to choose these coefficients when using the SLOPE on a general design matrix. A direct characterization of the posterior is provided which suggests a Gibbs sampler that does not involve latent variables. An efficient hybrid Gibbs sampler for the Bayesian SLOPE is introduced. Point estimation using the posterior mean is highlighted, which automatically facilitates the Bayesian prediction of future observations. These are demonstrated on real and synthetic data.

In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding divergences have been discussed. One of such divergences is the $\gamma$-divergence and the robust estimator using the $\gamma$-divergence is known for having a strong robustness. In this paper, we consider the robust and sparse regression based on $\gamma$-divergence. We extend the $\gamma$-divergence to the regression problem and show that it has a strong robustness under heavy contamination even when outliers are heterogeneous. The loss function is constructed by an empirical estimate of the $\gamma$-divergence with sparse regularization and the parameter estimate is defined as the minimizer of the loss function. To obtain the robust and sparse estimate, we propose an efficient update algorithm which has a monotone decreasing property of the loss function. Particularly, we discuss a linear regression problem with $L_1$ regularization in detail. In numerical experiments and real data analyses, we see that the proposed method outperforms past robust and sparse methods.

I am working on some practical articles on variable selection, especially in the context of step-wise linear regression and logistic regression. One thing I noticed while preparing some examples is that summaries such as model quality (especially out of sample quality) and variable significances are not quite as simple as one would hope (they in fact lack a lot of the monotone structure or submodular structure that would make things easy). That being said we have a lot of powerful and effective heuristics to discuss in upcoming articles. I am going to leave such positive results for my later articles and here concentrate on an instructive technical negative result: picking a good subset of variables is theoretically quite hard. When we say something is "theoretically hard" we mean we can contrive examples of it that encode instances of other problems thought to be hard.

Summary: We show in illustrations how the machine learning'training' process happens in Tensorflow, and tie them back to the Tensorflow code. This paves the way for discussing'training' variations, namely stochastic/mini-batch/batch, and adaptive learning rate gradient descent. The'training' variation code snippets presented serve to reinforce the understanding of the role of Tensorflow placeholders. In the previous article, we used Tensorflow (TF) to build and learn a linear regression model with a single feature so that given a feature value (house size/sqm), we can predict the outcome (house price/). In machine learning (ML) literature, we come across the term'training' very often, let us literally look at what that means in TF.

We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features. In general, sparse signal processing problems can be characterized in terms of the following Markovian property. We are given a set of $N$ variables $X_1,X_2,\ldots,X_N$, and there is an unknown subset of variables $S \subset \{1,\ldots,N\}$ that are relevant for predicting outcomes $Y$. More specifically, when $Y$ is conditioned on $\{X_n\}_{n\in S}$ it is conditionally independent of the other variables, $\{X_n\}_{n \not \in S}$. Our goal is to identify the set $S$ from samples of the variables $X$ and the associated outcomes $Y$. We characterize this problem as a version of the noisy channel coding problem. Using asymptotic information theoretic analyses, we establish mutual information formulas that provide sufficient and necessary conditions on the number of samples required to successfully recover the salient variables. These mutual information expressions unify conditions for both linear and nonlinear observations. We then compute sample complexity bounds for the aforementioned models, based on the mutual information expressions in order to demonstrate the applicability and flexibility of our results in general sparse signal processing models.

To construct flexible nonlinear predictive distributions, the paper introduces a family of softplus function based regression models that convolve, stack, or combine both operations by convolving countably infinite stacked gamma distributions, whose scales depend on the covariates. Generalizing logistic regression that uses a single hyperplane to partition the covariate space into two halves, softplus regressions employ multiple hyperplanes to construct a confined space, related to a single convex polytope defined by the intersection of multiple half-spaces or a union of multiple convex polytopes, to separate one class from the other. The gamma process is introduced to support the convolution of countably infinite (stacked) covariate-dependent gamma distributions. For Bayesian inference, Gibbs sampling derived via novel data augmentation and marginalization techniques is used to deconvolve and/or demix the highly complex nonlinear predictive distribution. Example results demonstrate that softplus regressions provide flexible nonlinear decision boundaries, achieving classification accuracies comparable to that of kernel support vector machine while requiring significant less computation for out-of-sample prediction.

This short tutorial will not only guide you through some basic data analysis methods but it will also show you how to implement some of the more sophisticated techniques available today. We will look into traffic accident data from the National Highway Traffic Safety Administration and try to predict fatal accidents using state-of-the-art statistical learning techniques. If you are interested, download the code at the bottom and follow along as we work through a real world data set. This post is in R while a companion post covers the same techniques in Python. The swirl package is designed to teach people R.