Understanding how species are distributed across landscapes over time is a fundamental question in biodiversity research. Unfortunately, most species distribution models only target a single species at a time, despite strong ecological evidence that species are not independently distributed. We propose Deep Multi-Species Embedding (DMSE), which jointly embeds vectors corresponding to multiple species as well as vectors representing environmental covariates into a common high-dimensional feature space via a deep neural network. Applied to bird observational data from the citizen science project \textit{eBird}, we demonstrate how the DMSE model discovers inter-species relationships to outperform single-species distribution models (random forests and SVMs) as well as competing multi-label models. Additionally, we demonstrate the benefit of using a deep neural network to extract features within the embedding and show how they improve the predictive performance of species distribution modelling. An important domain contribution of the DMSE model is the ability to discover and describe species interactions while simultaneously learning the shared habitat preferences among species. As an additional contribution, we provide a graphical embedding of hundreds of bird species in the Northeast US.

The method of "random Fourier features (RFF)" has become a popular tool for approximating the "radial basis function (RBF)" kernel. The variance of RFF is actually large. Interestingly, the variance can be substantially reduced by a simple normalization step as we theoretically demonstrate. We name the improved scheme as the "normalized RFF (NRFF)". We also propose the "generalized min-max (GMM)" kernel as a measure of data similarity. GMM is positive definite as there is an associated hashing method named "generalized consistent weighted sampling (GCWS)" which linearizes this nonlinear kernel. We provide an extensive empirical evaluation of the RBF kernel and the GMM kernel on more than 50 publicly available datasets. For a majority of the datasets, the (tuning-free) GMM kernel outperforms the best-tuned RBF kernel. We conduct extensive experiments for comparing the linearized RBF kernel using NRFF with the linearized GMM kernel using GCWS. We observe that, to reach a comparable classification accuracy, GCWS typically requires substantially fewer samples than NRFF, even on datasets where the original RBF kernel outperforms the original GMM kernel. The empirical success of GCWS (compared to NRFF) can also be explained from a theoretical perspective. Firstly, the relative variance (normalized by the squared expectation) of GCWS is substantially smaller than that of NRFF, except for the very high similarity region (where the variances of both methods are close to zero). Secondly, if we make a model assumption on the data, we can show analytically that GCWS exhibits much smaller variance than NRFF for estimating the same object (e.g., the RBF kernel), except for the very high similarity region.

Recently, I did a session at local user group in Ljubljana, Slovenija, where I introduced the new algorithms that are available with MicrosoftML package for Microsoft R Server 9.0.3. For dataset, I have used two from (still currently) running sessions from Kaggle. In the last part, I did image detection and prediction of MNIST dataset and compared the performance and accuracy between. MNIST Handwritten digit database is available here. Starting off with rxNeuralNet, we have to build a NET# model or Neural network to work it's way.

We consider i.i.d. samples $x_1, \dots, x_n$ from a measure $\nu$ with density supported on a bounded Euclidean domain $D \subseteq R^d $ where $d\geq3$. A graph on the point cloud is obtained by connecting two points if one of them is among the $k$-nearest neighbors of the other. Our goal is to study consistency of graph based procedures to clustering, classification and dimensionality reduction by studying the variational convergence of the graph total variation associated to such $k$-NN graph. We prove that provided $k:=k_n$ scales like $n \gg k_n \gg \log(n)$, then the $\Gamma$-convergence of the graph total variation towards an appropriate weighted total variation is guaranteed.

This paper provides asymptotic theory for Inverse Probability Weighing (IPW) and Locally Robust Estimator (LRE) of Best Linear Predictor where the response missing at random (MAR), but not completely at random (MCAR). We relax previous assumptions in the literature about the first-step nonparametric components, requiring only their mean square convergence. This relaxation allows to use a wider class of machine leaning methods for the first-step, such as lasso. For a generic first-step, IPW incurs a first-order bias unless the model it approximates is truly linear in the predictors. In contrast, LRE remains first-order unbiased provided one can estimate the conditional expectation of the response with sufficient accuracy. An additional novelty is allowing the dimension of Best Linear Predictor to grow with sample size. These relaxations are important for estimation of best linear predictor of teacher-specific and hospital-specific effects with large number of individuals.

Successful analysis of player skills in video games has important impacts on the process of enhancing player experience without undermining their continuous skill development. Moreover, player skill analysis becomes more intriguing in team-based video games because such form of study can help discover useful factors in effective team formation. In this paper, we consider the problem of skill decomposition in MOBA (MultiPlayer Online Battle Arena) games, with the goal to understand what player skill factors are essential for the outcome of a game match. To understand the construct of MOBA player skills, we utilize various skill-based predictive models to decompose player skills into interpretative parts, the impact of which are assessed in statistical terms. We apply this analysis approach on two widely known MOBAs, namely League of Legends (LoL) and Defense of the Ancients 2 (DOTA2). The finding is that base skills of in-game avatars, base skills of players, and players' champion-specific skills are three prominent skill components influencing LoL's match outcomes, while those of DOTA2 are mainly impacted by in-game avatars' base skills but not much by the other two.

Concentration inequalities are indispensable tools for studying the generalization capacity of learning models. Hoeffding's and McDiarmid's inequalities are commonly used, giving bounds independent of the data distribution. Although this makes them widely applicable, a drawback is that the bounds can be too loose in some specific cases. Although efforts have been devoted to improving the bounds, we find that the bounds can be further tightened in some distribution-dependent scenarios and conditions for the inequalities can be relaxed. In particular, we propose four types of conditions for probabilistic boundedness and bounded differences, and derive several distribution-dependent extensions of Hoeffding's and McDiarmid's inequalities. These extensions provide bounds for functions not satisfying the conditions of the existing inequalities, and in some special cases, tighter bounds. Furthermore, we obtain generalization bounds for unbounded and hierarchy-bounded loss functions. Finally we discuss the potential applications of our extensions to learning theory.

This paper presents an alternative approach to p-values in regression settings. This approach, whose origins can be traced to machine learning, is based on the leave-one-out bootstrap for prediction error. In machine learning this is called the out-of-bag (OOB) error. To obtain the OOB error for a model, one draws a bootstrap sample and fits the model to the in-sample data. The out-of-sample prediction error for the model is obtained by calculating the prediction error for the model using the out-of-sample data. Repeating and averaging yields the OOB error, which represents a robust cross-validated estimate of the accuracy of the underlying model. By a simple modification to the bootstrap data involving "noising up" a variable, the OOB method yields a variable importance (VIMP) index, which directly measures how much a specific variable contributes to the prediction precision of a model. VIMP provides a scientifically interpretable measure of the effect size of a variable, we call the "predictive effect size", that holds whether the researcher's model is correct or not, unlike the p-value whose calculation is based on the assumed correctness of the model. We also discuss a marginal VIMP index, also easily calculated, which measures the marginal effect of a variable, or what we call "the discovery effect". The OOB procedure can be applied to both parametric and nonparametric regression models and requires only that the researcher can repeatedly fit their model to bootstrap and modified bootstrap data. We illustrate this approach on a survival data set involving patients with systolic heart failure and to a simulated survival data set where the model is incorrectly specified to illustrate its robustness to model misspecification.

We tightly analyze the sample complexity of CCA, provide a learning algorithm that achieves optimal statistical performance in time linear in the required number of samples (up to log factors), as well as a streaming algorithm with similar guarantees.

This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=||^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of measurements is significantly smaller than the dimension of the signal ($m<