The support vector machine (SVM) and minimum Euclidean norm least squares regression are two fundamentally different approaches to fitting linear models, but they have recently been connected in models for very high-dimensional data through a phenomenon of support vector proliferation, where every training example used to fit an SVM becomes a support vector. In this paper, we explore the generality of this phenomenon and make the following contributions. First, we prove a super-linear lower bound on the dimension (in terms of sample size) required for support vector proliferation in independent feature models, matching the upper bounds from previous works. We further identify a sharp phase transition in Gaussian feature models, bound the width of this transition, and give experimental support for its universality. Finally, we hypothesize that this phase transition occurs only in much higher-dimensional settings in the ℓ1 variant of the SVM, and we present a new geometric characterization of the problem that may elucidate this phenomenon for the general ℓp case.

Figure 8: Visualizations of accuracy and bias flows for the smaller ANN trained on the synthetic dataset. Note how the most dominant accuracy flows arise from X3, which is the only bias-free feature in the dataset. In contrast, the largest bias flows arise from X1 and X2, both of which are heavily biased features. It is intuitively clear from these pictures which edges have the largest bias-to-accuracy flow ratios, and hence which edges would be the first to be pruned.

Motivated by neuroscientific and clinical applications, we empirically examine whether observational measures of information flow can suggest interventions. We do so by performing experiments on artificial neural networks in the context of fairness in machine learning, where the goal is to induce fairness in the system through interventions. Using our recently developed M-information flow framework, we measure the flow of information about the true label (responsible for accuracy, and hence desirable), and separately, the flow of information about a protected attribute (responsible for bias, and hence undesirable) on the edges of a trained neural network. We then compare the flow magnitudes against the effect of intervening on those edges by pruning. We show that pruning edges that carry larger information flows about the protected attribute reduces bias at the output to a greater extent. This demonstrates that M-information flow can meaningfully suggest targets for interventions, answering the title's question in the affirmative. We also evaluate bias-accuracy tradeoffs for different intervention strategies, to analyze how one might use estimates of desirable and undesirable information flows (here, accuracy and bias flows) to inform interventions that preserve the former while reducing the latter.

We introduce a new general identifiable framework for principled disentanglement referred to as Structured Nonlinear Independent Component Analysis (SNICA). Our contribution is to extend the identifiability theory of deep generative models for a very broad class of structured models. While previous works have shown identifiability for specific classes of time-series models, our theorems extend this to more general temporal structures as well as to models with more complex structures such as spatial dependencies. In particular, we establish the major result that identifiability for this framework holds even in the presence of noise of unknown distribution. Finally, as an example of our framework's flexibility, we introduce the first nonlinear ICA model for time-series that combines the following very useful properties: it accounts for both nonstationarity and autocorrelation in a fully unsupervised setting; performs dimensionality reduction; models hidden states; and enables principled estimation and inference by variational maximum-likelihood.

C.2 Consolidated CV with random features Alternatively, one can use random features (Rahimi and Recht, 2007) to approximate the kernel matrix. Suppose that we consider shift-invariant kernels that satisfy K(x,y) = K(x y). In this work we use the radial kernel K(x,y) = exp( σ x y 22). The kernel can be approximated by K(x,y) φ(x),φ(y), where an explicit randomized feature mapping φ: IRp IRm is obtained by sampling from a distribution defined by the inverse Fourier transformation.

We develop methods for rapidly identifying important components of a convex optimization problem for the purpose of achieving fast convergence times. By considering a novel problem formulation--the minimization of a sum of piecewise functions--we describe a principled and general mechanism for exploiting piecewise linear structure in convex optimization. This result leads to a theoretically justified working set algorithm and a novel screening test, which generalize and improve upon many prior results on exploiting structure in convex optimization. In empirical comparisons, we study the scalability of our methods. We find that screening scales surprisingly poorly with the size of the problem, while our working set algorithm convincingly outperforms alternative approaches.

Recently proposed adversarial classification methods have shown promising results for cost sensitive and multivariate losses. In contrast with empirical risk minimization (ERM) methods, which use convex surrogate losses to approximate the desired non-convex target loss function, adversarial methods minimize non-convex losses by treating the properties of the training data as being uncertain and worst case within a minimax game. Despite this difference in formulation, we recast adversarial classification under zero-one loss as an ERM method with a novel prescribed loss function. We demonstrate a number of theoretical and practical advantages over the very closely related hinge loss ERM methods. This establishes adversarial classification under the zero-one loss as a method that fills the long standing gap in multiclass hinge loss classification, simultaneously guaranteeing Fisher consistency and universal consistency, while also providing dual parameter sparsity and high accuracy predictions in practice.