Machine learning (ML) is the current paradigm for modeling statistical phenomena by harnessing algorithms that exploit computer intelligence. It is common place to build ML models that predict housing prices, aggregate users by their potential marketing interests, and use image recognition techniques to identify brain tumors. However, up until now these models have required scrupulous trial and error in order to optimize model performance on unseen data. The advent of automated machine learning (AutoML) aims to curb the resources required (time and expertise) by offering well-designed pipelines that handle data preprocessing, feature selection, and model creation and evaluation. While AutoML may initially only appeal to enterprises that want to harness the power of ML without consuming precious budgets and hiring skilled data practitioners, it also contains very strong promise to become an invaluable tool for the experienced data scientist.

Insufficient capability of existing subspace clustering methods to handle data coming from nonlinear manifolds, data corruptions, and out-of-sample data hinders their applicability to address real-world clustering and classification problems. This paper proposes the robust formulation of the self-supervised convolutional subspace clustering network ($S^2$ConvSCN) that incorporates the fully connected (FC) layer and, thus, it is capable for handling out-of-sample data by classifying them using a softmax classifier. $S^2$ConvSCN clusters data coming from nonlinear manifolds by learning the linear self-representation model in the feature space. Robustness to data corruptions is achieved by using the correntropy induced metric (CIM) of the error. Furthermore, the block-diagonal (BD) structure of the representation matrix is enforced explicitly through BD regularization. In a truly unsupervised training environment, Robust $S^2$ConvSCN outperforms its baseline version by a significant amount for both seen and unseen data on four well-known datasets. Arguably, such an ablation study has not been reported before.

We introduce a new primal-dual algorithm for minimizing the sum of three convex functions, each of which has its own oracle. Namely, the first one is differentiable, smooth and possibly stochastic, the second is proximable, and the last one is a composition of a proximable function with a linear map. Our theory covers several settings that are not tackled by any existing algorithm; we illustrate their importance with real-world applications. By leveraging variance reduction, we obtain convergence with linear rates under strong convexity and fast sublinear convergence under convexity assumptions. The proposed theory is simple and unified by the umbrella of stochastic Davis-Yin splitting, which we design in this work. Finally, we illustrate the efficiency of our method through numerical experiments.

Adversarial training is a common approach to improving the robustness of deep neural networks against adversarial examples. In this work, we propose a novel regularization approach as an alternative. To derive the regularizer, we formulate the adversarial robustness problem under the robust optimization framework and approximate the loss function using a second-order Taylor series expansion. Our proposed second-order adversarial regularizer (SOAR) is an upper bound based on the Taylor approximation of the inner-max in the robust optimization objective. We empirically show that the proposed method improves the robustness of networks on the CIFAR-10 dataset.

We formalize an equivalence between two popular methods for Bayesian inference: Stein variational gradient descent (SVGD) and black-box variational inference (BBVI). In particular, we show that BBVI corresponds precisely to SVGD when the kernel is the neural tangent kernel. Furthermore, we interpret SVGD and BBVI as kernel gradient flows; we do this by leveraging the recent perspective that views SVGD as a gradient flow in the space of probability distributions and showing that BBVI naturally motivates a Riemannian structure on that space. We observe that kernel gradient flow also describes dynamics found in the training of generative adversarial networks (GANs). This work thereby unifies several existing techniques in variational inference and generative modeling and identifies the kernel as a fundamental object governing the behavior of these algorithms, motivating deeper analysis of its properties.

The objective of this study is to predict suicidal and non-suicidal deaths from DNA methylation data using a modern machine learning algorithm. We used support vector machines to classify existing secondary data consisting of normalized values of methylated DNA probe intensities from tissues of two cortical brain regions to distinguish suicide cases from control cases. Before classification, we employed Principal component analysis (PCA) and t-distributed Stochastic Neighbor Embedding (t-SNE) to reduce the dimension of the data. In comparison to PCA, the modern data visualization method t-SNE performs better in dimensionality reduction. t-SNE accounts for the possible non-linear patterns in low-dimensional data. We applied four-fold cross-validation in which the resulting output from t-SNE was used as training data for the Support Vector Machine (SVM). Despite the use of cross-validation, the nominally perfect prediction of suicidal deaths for BA11 data suggests possible over-fitting of the model. The study also may have suffered from 'spectrum bias' since the individuals were only studied from two extreme scenarios. This research constitutes a baseline study for classifying suicidal and non-suicidal deaths from DNA methylation data. Future studies with larger sample size, while possibly incorporating methylation data from living individuals, may reduce the bias and improve the accuracy of the results.

This study uses stacked generalization, which is a two-step process of combining machine learning methods, called meta or super learners, for improving the performance of algorithms in step one (by minimizing the error rate of each individual algorithm to reduce its bias in the learning set) and then in step two inputting the results into the meta learner with its stacked blended output (demonstrating improved performance with the weakest algorithms learning better). The method is essentially an enhanced cross-validation strategy. Although the process uses great computational resources, the resulting performance metrics on resampled fraud data show that increased system cost can be justified. A fundamental key to fraud data is that it is inherently not systematic and, as of yet, the optimal resampling methodology has not been identified. Building a test harness that accounts for all permutations of algorithm sample set pairs demonstrates that the complex, intrinsic data structures are all thoroughly tested. Using a comparative analysis on fraud data that applies stacked generalizations provides useful insight needed to find the optimal mathematical formula to be used for imbalanced fraud data sets.

We propose orthogonal inductive matrix completion (OMIC), an interpretable model composed of a sum of matrix completion terms, each with orthonormal side information. We can inject prior knowledge about the eigenvectors of the ground truth matrix, whilst maintaining the representation capability of the model. We present a provably converging algorithm that optimizes all components of the model simultaneously, using nuclear-norm regularisation. Our method is backed up by \textit{distribution-free} learning guarantees that improve with the quality of the injected knowledge. As a special case of our general framework, we study a model consisting of a sum of user and item biases (generic behaviour), a non-inductive term (specific behaviour), and an inductive term using side information. Our theoretical analysis shows that $\epsilon$-recovering the ground truth matrix requires at most $O\left( \frac{n+m+(\sqrt{n}+\sqrt{m})mn \sqrt{r}C}{\epsilon^2}\right)$ entries, where $r$ is the rank of the ground truth matrix. We analyse the performance of OMIC on several synthetic and real datasets. On synthetic datasets with a sliding scale of user bias relevance, we show that OMIC better adapts to different regimes than other methods and can recover the ground truth. On real life datasets containing user/items recommendations and relevant side information, we find that OMIC surpasses the state of the art, with the added benefit of greater interpretability.

The vast majority of machine learning algorithms involve two different sets of parameters: the training parameters and the meta-parameters (also known as hyperparameters). While the training parameters are learned during the training phase, the values of the hyperparameters have to be specified before the learning phase. For instance, the hyperparameters of neural networks typically specify the architecture of the network (number and type of layers, number and type of nodes, etc). Determining the optimal combination of hyperparameter values leading to the best generalization performance can be done through repeated training and evaluation sessions, trying different combinations of hyperparameter values. We call each training evaluation process for one combination of hyperparameter values a trial. Each trial is computationally expensive, since it involves retraining the model.

We develop a method for uniform valid confidence bands of a nonparametric component $f_1$ in the general additive model $Y=f_1(X_1)+\ldots + f_p(X_p) + \varepsilon$ in a high-dimensional setting. We employ sieve estimation and embed it in a high-dimensional Z-estimation framework allowing us to construct uniformly valid confidence bands for the first component $f_1$. As usual in high-dimensional settings where the number of regressors $p$ may increase with sample, a sparsity assumption is critical for the analysis. We also run simulations studies which show that our proposed method gives reliable results concerning the estimation properties and coverage properties even in small samples. Finally, we illustrate our procedure with an empirical application demonstrating the implementation and the use of the proposed method in practice.