Extracting characteristics from the training datasets of classification problems has proven effective in a number of meta-analyses. Among them, measures of classification complexity can estimate the difficulty in separating the data points into their expected classes. Descriptors of the spatial distribution of the data and estimates of the shape and size of the decision boundary are among the existent measures for this characterization. This information can support the formulation of new data-driven pre-processing and pattern recognition techniques, which can in turn be focused on challenging characteristics of the problems. This paper surveys and analyzes measures which can be extracted from the training datasets in order to characterize the complexity of the respective classification problems. Their use in recent literature is also reviewed and discussed, allowing to prospect opportunities for future work in the area. Finally, descriptions are given on an R package named Extended Complexity Library (ECoL) that implements a set of complexity measures and is made publicly available.

Adaptive stochastic gradient descent methods, such as AdaGrad, Adam, AdaDelta, Nadam, AMSGrad, \textit{etc.}, have been demonstrated efficacious in solving non-convex stochastic optimization, such as training deep neural networks. However, their convergence rates have not been touched under the non-convex stochastic circumstance except recent breakthrough results on AdaGrad \cite{ward2018adagrad} and perturbed AdaGrad \cite{li2018convergence}. In this paper, we propose two new adaptive stochastic gradient methods called AdaHB and AdaNAG which integrate coordinate-wise AdaGrad with heavy ball momentum and Nesterov accelerated gradient momentum, respectively. The $\mathcal{O}(\frac{\log{T}}{\sqrt{T}})$ non-asymptotic convergence rates of AdaHB and AdaNAG in non-convex stochastic setting are also jointly characterized by leveraging a newly developed unified formulation of these two momentum mechanisms. In particular, when momentum term vanishes we obtain convergence rate of coordinate-wise AdaGrad in non-convex stochastic setting as a byproduct.

Boosting refers to a type of classification and regression algorithms that enjoy large popularity due to their excellent predictive accuracy on a wide range of datasets. The first boosting algorithms for classification, including the well known AdaBoost algorithm, were introduced by Schapire [1990], Freund and Schapire [1995], and Freund et al. [1996]. Later, several authors [Breiman, 1998, 1999, Friedman et al., 2000, Mason et al., 2000, Friedman, 2001] introduced the statistical view of boosting as a stagewise optimization approach. In particular, Friedman et al. [2000] first introduced boosting algorithms which iteratively optimize Bernoulli and multinomial likelihoods for binary and multiclass classification using Newton updates. Further, Friedman [2001] presented gradient descent based boosting algorithms for both regression and classification tasks with general loss functions.

We present two related methods for deriving connectivity-based brain atlases from individual connectomes. The proposed methods exploit a previously proposed dense connectivity representation, termed continuous connectivity, by first performing graph-based hierarchical clustering of individual brains, and subsequently aggregating the individual parcellations into a consensus parcellation. The search for consensus minimizes the sum of cluster membership distances, effectively estimating a pseudo-Karcher mean of individual parcellations. We assess the quality of our parcellations using (1) Kullback-Liebler and Jensen-Shannon divergence with respect to the dense connectome representation, (2) inter-hemispheric symmetry, and (3) performance of the simplified connectome in a biological sex classification task. We find that the parcellation based-atlas computed using a greedy search at a hierarchical depth 3 outperforms all other parcellation-based atlases as well as the standard Dessikan-Killiany anatomical atlas in all three assessments.

Machine learning models have been widely used in security applications such as intrusion detection, spam filtering, and virus or malware detection. However, it is well-known that adversaries are always trying to adapt their attacks to evade detection. For example, an email spammer may guess what features spam detection models use and modify or remove those features to avoid detection. There has been some work on making machine learning models more robust to such attacks. However, one simple but promising approach called {\em randomization} is underexplored. This paper proposes a novel randomization-based approach to improve robustness of machine learning models against evasion attacks. The proposed approach incorporates randomization into both model training time and model application time (meaning when the model is used to detect attacks). We also apply this approach to random forest, an existing ML method which already has some degree of randomness. Experiments on intrusion detection and spam filtering data show that our approach further improves robustness of random-forest method. We also discuss how this approach can be applied to other ML models.

We present a method for metric optimization in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, by treating the induced Riemannian metric on the space of diffeomorphisms as a kernel in a machine learning context. For simplicity, we choose the kernel Fischer Linear Discriminant Analysis (KLDA) as the framework. Optimizing the kernel parameters in an Expectation-Maximization framework, we define model fidelity via the hinge loss of the decision function. The resulting algorithm optimizes the parameters of the LDDMM norm-inducing differential operator as a solution to a group-wise registration and classification problem. In practice, this may lead to a biology-aware registration, focusing its attention on the predictive task at hand such as identifying the effects of disease. We first tested our algorithm on a synthetic dataset, showing that our parameter selection improves registration quality and classification accuracy. We then tested the algorithm on 3D subcortical shapes from the Schizophrenia cohort Schizconnect. Our Schizpohrenia-Control predictive model showed significant improvement in ROC AUC compared to baseline parameters.

In this paper we introduce a new machine learning (ML) model for nonlinear regression called Boosting Smooth Transition Regression Tree (BooST). The main advantage of the BooST is that it estimates the derivatives (partial effects) of very general nonlinear models, providing more interpretation than other tree based models concerning the mapping between the covariates and the dependent variable. We provide some asymptotic theory that shows consistency of the partial derivatives and we present some examples on simulated and empirical data.

The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as classical inverse or filtering problems and, furthermore, we propose an efficient, gradient-free algorithm for finding a solution to these problems using ensemble Kalman inversion (EKI). Applications of our approach include offline and online supervised learning with deep neural networks, as well as graph-based semi-supervised learning. The essence of the EKI procedure is an ensemble based approximate gradient descent in which derivatives are replaced by differences from within the ensemble. We suggest several modifications to the basic method, derived from empirically successful heuristics developed in the context of SGD. Numerical results demonstrate wide applicability and robustness of the proposed algorithm.

This database provided a comprehensive record of opioids dispensed at California pharmacies to civilian, non–U.S. Department of Veterans Affairs, and non-institutionalized patients treated by clinicians in our sample. Descriptive and inferential statistics were carried out with the Stata software (6). The cmp command in Stata was used to compute a difference-in-differences estimator within a mixed-model two-part linear regression analysis (7). The difference-in-differences estimator compared the average change over time in milligram morphine equivalents (MMEs) dispensed for prescribers in the intervention group with the average change over time for prescribers in the control group.

Our initial results look promising, but there is room for improvement. We made a number of choices and assumptions for our initial analysis. Our next steps would be to go back and evaluate these to determine what changes we can make to tune our classifier. If we plan to use this classifier for a real-time credit card fraud detection system, we want to ensure that we can catch all the fraudulent transactions and also keep our customers happy by correctly identifying non-fraudulent transactions. Once we have a good classifier, we can use it directly with transactions arriving into Ignite in real-time. Additionally, with Ignite's continuous learning capabilities, we can refine and tune our classifier further with new data, as the data arrive. Finally, using Ignite as the basis for a real-time fraud detection system enables us to obtain many advantages, such as the ability to scale ML processing beyond a single node, the storage and manipulation of massive quantities of data, and zero ETL.