Have you ever looked at a machine learning classification model and thought, I could have made that? Well, that is what we test in this project, comparing XGBoost trained on human engineered features to training directly on data. The human engineered features do not outperform XGBoost trained di- rectly on the data, but they are comparable. This project con- tributes a novel method for utilizing human created classifi- cation models on high dimensional datasets.

Probabilistic-driven classification techniques extend the role of traditional approaches that output labels (usually integer numbers) only. Such techniques are more fruitful when dealing with problems where one is not interested in recognition/identification only, but also into monitoring the behavior of consumers and/or machines, for instance. Therefore, by means of probability estimates, one can take decisions to work better in a number of scenarios. In this paper, we propose a probabilistic-based Optimum Path Forest (OPF) classifier to handle with binary classification problems, and we show it can be more accurate than naive OPF in a number of datasets. In addition to being just more accurate or not, probabilistic OPF turns to be another useful tool to the scientific community.

This article is featured in the new DZone Guide to Big Data Processing, Volume III. Get your free copy for more insightful articles, industry statistics, and more. In the past few decades, computer systems have achieved a whole lot. They have managed to organize and catalog the information produced by our civilization as a whole. They have relieved us from stringent cognitive tasks and increased our productivity significantly. One could say that where the industrial revolution automated labor, the digital revolution has automated cognitive labor. This statement isn't entirely correct however, if it was we would all be without a job.

Large-scale generalized linear array models (GLAMs) can be challenging to fit. Computation and storage of its tensor product design matrix can be impossible due to time and memory constraints, and previously considered design matrix free algorithms do not scale well with the dimension of the parameter vector. A new design matrix free algorithm is proposed for computing the penalized maximum likelihood estimate for GLAMs, which, in particular, handles nondifferentiable penalty functions. The proposed algorithm is implemented and available via the R package \verb+glamlasso+. It combines several ideas -- previously considered separately -- to obtain sparse estimates while at the same time efficiently exploiting the GLAM structure. In this paper the convergence of the algorithm is treated and the performance of its implementation is investigated and compared to that of \verb+glmnet+ on simulated as well as real data. It is shown that the computation time for

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.

We consider the problem of recovering a complete (i.e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb{R}^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse. This recovery problem is central to theoretical understanding of dictionary learning, which seeks a sparse representation for a collection of input signals and finds numerous applications in modern signal processing and machine learning. We give the first efficient algorithm that provably recovers $\mathbf A_0$ when $\mathbf X_0$ has $O(n)$ nonzeros per column, under suitable probability model for $\mathbf X_0$. In contrast, prior results based on efficient algorithms either only guarantee recovery when $\mathbf X_0$ has $O(\sqrt{n})$ zeros per column, or require multiple rounds of SDP relaxation to work when $\mathbf X_0$ has $O(n^{1-\delta})$ nonzeros per column (for any constant $\delta \in (0, 1)$). } Our algorithmic pipeline centers around solving a certain nonconvex optimization problem with a spherical constraint. In this paper, we provide a geometric characterization of the objective landscape. In particular, we show that the problem is highly structured: with high probability, (1) there are no "spurious" local minimizers; and (2) around all saddle points the objective has a negative directional curvature. This distinctive structure makes the problem amenable to efficient optimization algorithms. In a companion paper (arXiv:1511.04777), we design a second-order trust-region algorithm over the sphere that provably converges to a local minimizer from arbitrary initializations, despite the presence of saddle points.

In most classification tasks there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classification allows the classifiers to output a set of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framework for multiclass set-valued classification, where the classifiers guarantee user-defined levels of coverage or confidence (the probability that the true label is contained in the set) while minimizing the ambiguity (the expected size of the output). We first derive oracle classifiers assuming the true distribution to be known. We show that the oracle classifiers are obtained from level sets of the functions that define the conditional probability of each class. Then we develop estimators with good asymptotic and finite sample properties. The proposed classifiers build on and refine many existing single-label classifiers. The optimal classifier can sometimes output the empty set. We provide two solutions to fix this issue that are suitable for various practical needs.

In this paper, we study the challenge of feature selection based on a relatively small collection of sample pairs $\{(x_i, y_i)\}_{1 \leq i \leq m}$. The observations $y_i \in \mathbb{R}$ are thereby supposed to follow a noisy single-index model, depending on a certain set of signal variables. A major difficulty is that these variables usually cannot be observed directly, but rather arise as hidden factors in the actual data vectors $x_i \in \mathbb{R}^d$ (feature variables). We will prove that a successful variable selection is still possible in this setup, even when the applied estimator does not have any knowledge of the underlying model parameters and only takes the 'raw' samples $\{(x_i, y_i)\}_{1 \leq i \leq m}$ as input. The model assumptions of our results will be fairly general, allowing for non-linear observations, arbitrary convex signal structures as well as strictly convex loss functions. This is particularly appealing for practical purposes, since in many applications, already standard methods, e.g., the Lasso or logistic regression, yield surprisingly good outcomes. Apart from a general discussion of the practical scope of our theoretical findings, we will also derive a rigorous guarantee for a specific real-world problem, namely sparse feature extraction from (proteomics-based) mass spectrometry data.

Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-case (i.e., adversarial) perturbations of the datapoints. On the other hand, it has been empirically observed that these same classifiers are relatively robust to random noise. In this paper, we propose to study a \textit{semi-random} noise regime that generalizes both the random and worst-case noise regimes. We propose the first quantitative analysis of the robustness of nonlinear classifiers in this general noise regime. We establish precise theoretical bounds on the robustness of classifiers in this general regime, which depend on the curvature of the classifier's decision boundary. Our bounds confirm and quantify the empirical observations that classifiers satisfying curvature constraints are robust to random noise. Moreover, we quantify the robustness of classifiers in terms of the subspace dimension in the semi-random noise regime, and show that our bounds remarkably interpolate between the worst-case and random noise regimes. We perform experiments and show that the derived bounds provide very accurate estimates when applied to various state-of-the-art deep neural networks and datasets. This result suggests bounds on the curvature of the classifiers' decision boundaries that we support experimentally, and more generally offers important insights onto the geometry of high dimensional classification problems.