Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points. These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property.

Large labeled training sets are the critical building blocks of supervised learning methods and are key enablers of deep learning techniques. For some applications, creating labeled training sets is the most time-consuming and expensive part of applying machine learning. We therefore propose a paradigm for the programmatic creation of training sets called data programming in which users provide a set of labeling functions, which are programs that heuristically label subsets of the data, but that are noisy and may conflict. By viewing these labeling functions as implicitly describing a generative model for this noise, we show that we can recover the parameters of this model to "denoise" the generated training set, and establish theoretically that we can recover the parameters of these generative models in a handful of settings. We then show how to modify a discriminative loss function to make it noise-aware, and demonstrate our method over a range of discriminative models including logistic regression and LSTMs.

We establish upper and lower bounds for the influence of a set of nodes in certain types of contagion models. We derive two sets of bounds, the first designed for linear threshold models, and the second more broadly applicable to a general class of triggering models, which subsumes the popular independent cascade models, as well. We quantify the gap between our upper and lower bounds in the case of the linear threshold model and illustrate the gains of our upper bounds for independent cascade models in relation to existing results. Importantly, our lower bounds are monotonic and submodular, implying that a greedy algorithm for influence maximization is guaranteed to produce a maximizer within a (1 - 1/e)-factor of the truth. Although the problem of exact influence computation is NP-hard in general, our bounds may be evaluated efficiently.

Exemplar learning is a powerful paradigm for discovering visual similarities in an unsupervised manner. In this context, however, the recent breakthrough in deep learning could not yet unfold its full potential. With only a single positive sample, a great imbalance between one positive and many negatives, and unreliable relationships between most samples, training of convolutional neural networks is impaired. Given weak estimates of local distance we propose a single optimization problem to extract batches of samples with mutually consistent relations. Conflicting relations are distributed over different batches and similar samples are grouped into compact cliques.

We provide tight upper and lower bounds on the complexity of minimizing the average of m convex functions using gradient and prox oracles of the component functions. We show a significant gap between the complexity of deterministic vs randomized optimization. For smooth functions, we show that accelerated gradient descent (AGD) and an accelerated variant of SVRG are optimal in the deterministic and randomized settings respectively, and that a gradient oracle is sufficient for the optimal rate. For non-smooth functions, having access to prox oracles reduces the complexity and we present optimal methods based on smoothing that improve over methods using just gradient accesses.

Breakthroughs, discoveries, and DIY tips sent every weekday. Gravity seems like a predictable, even mundane, aspect of existence. The physics dictating one of the universe's four fundamental forces is relatively straightforward to understand and calculate (most of the time, at least). Even so, the relationships between objects with mass and energy continues to surprise physical engineers. Take recent observations made by a team at the University of Waterloo, for example.

We study fast learning rates when the losses are not necessarily bounded and may have a distribution with heavy tails. To enable such analyses, we introduce two new conditions: (i) the envelope function \sup_{f \in \mathcal{F}} \ell \circ f, where \ell is the loss function and \mathcal{F} is the hypothesis class, exists and is L r -integrable, and (ii) \ell satisfies the multi-scale Bernstein's condition on \mathcal{F} . Under these assumptions, we prove that learning rate faster than O(n {-1/2}) can be obtained and, depending on r and the multi-scale Bernstein's powers, can be arbitrarily close to O(n {-1}) . We then verify these assumptions and derive fast learning rates for the problem of vector quantization by k -means clustering with heavy-tailed distributions. The analyses enable us to obtain novel learning rates that extend and complement existing results in the literature from both theoretical and practical viewpoints.

In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function \func . Traditional methods for this problem assume just the availability of this single function. However, in many cases, cheap approximations to \func may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of \func in a small but promising region and speedily identify the optimum.

Probabilistic prediction aims to compute predictive distributions rather than single point predictions. These distributions enable practitioners to quantify uncertainty, compute risk, and detect outliers. However, most probabilistic methods assume parametric responses, such as Gaussian or Poisson distributions. When these assumptions fail, such models lead to bad predictions and poorly calibrated uncertainty. In this paper, we propose Treeffuser, an easy-to-use method for probabilistic prediction on tabular data.

This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification. The central theme of this work is establishing equivalences between learnability and compressibility, and utilizing these equivalences in the study of statistical learning theory. We begin with the setting of multiclass categorization (zero/one loss). We prove that in this case learnability is equivalent to compression of logarithmic sample size, and that uniform convergence implies compression of constant size. We then consider Vapnik's general learning setting: we show that in order to extend the compressibility-learnability equivalence to this case, it is necessary to consider an approximate variant of compression. Finally, we provide some applications of the compressibility-learnability equivalences.