When food delivery services talk breathlessly about machine learning, feel free to roll your eyes: it's baked salmon they're dropping off, not Bayesian statistics. Insurance is another kettle of fish altogether. The birth of statistics is usually dated to 1662, when John Graunt calculated the probabilities of Londoners surviving to a given age. Lloyds of London started shortly thereafter, and advances in statistics and insurance have been inseparable ever since. But in recent years, supremacy in statistics has moved to Silicon Valley – a bad omen for the insurance establishment.

ABSTRACT Diffusion maps are an emerging data-driven technique for nonlinear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. Thus, long time-series data presents a significant challenge for fast and efficient embedding. We propose integrating the Nystr om method with diffusion maps in order to ease the computational demand. We achieve a speedup of roughly two to four times when approximating the dominant diffusion map components. Index Terms-- Dimension Reduction, Nystr om method 1. MOTIV A TION In the era of'big data', dimension reduction is critical for data science.

Words: 4252 Keywords: self-monitoring data, type 2 diabetes, machine learning, phenotyping, precision medicine ABSTRACT Objective: To evaluate unsupervised clustering methods for identifying individual-level behavioral-clinical phenotypes that relate personal biomarkers and behavioral traits in type 2 diabetes (T2DM) self-monitoring data. Materials and Methods: We used hierarchical clustering (HC) to identify groups of meals with similar nutrition and glycemic impact for 6 individuals with T2DM who collected self-monitoring data. We evaluated clusters on: 1) correspondence to gold standards generated by certified diabetes educators (CDEs) for 3 participants; 2) face validity, rated by CDEs, and 3) impact on CDEs' ability to identify patterns for another 3 participants. Results: Gold standard (GS) included 9 patterns across 3 participants. Of these, all 9 were rediscovered using HC: 4 GS patterns were consistent with patterns identified by HC (over 50% of meals in a cluster followed the pattern); another 5 were included as subgroups in broader clusers. After reviewing clusters, CDEs identified patterns that were more consistent with data (70% reduction in contradictions between patterns and participants' records). Discussion: Hierarchical clustering of blood glucose and macronutrient consumption appears suitable for discovering behavioral-clinical phenotypes in T2DM. Most clusters corresponded to gold standard and were rated positively by CDEs for face validity. Cluster visualizations helped CDEs identify more robust patterns in nutrition and glycemic impact, creating new possibilities for visual analytic solutions. Conclusion: Machine learning methods can use diabetes self-monitoring data to create personalized behavioral-clinical phenotypes, which may prove useful for delivering personalized medicine.

We consider the problem of contextual bandits with stochastic experts, which is a variation of the traditional stochastic contextual bandit with experts problem. In our problem setting, we assume access to a class of stochastic experts, where each expert is a conditional distribution over the arms given a context. We propose upper-confidence bound (UCB) algorithms for this problem, which employ two different importance sampling based estimators for the mean reward for each expert. Both these estimators leverage information leakage among the experts, thus using samples collected under all the experts to estimate the mean reward of any given expert. This leads to instance dependent regret bounds of $\mathcal{O}\left(\lambda(\pmb{\mu})\mathcal{M}\log T/\Delta \right)$, where $\lambda(\pmb{\mu})$ is a term that depends on the mean rewards of the experts, $\Delta$ is the smallest gap between the mean reward of the optimal expert and the rest, and $\mathcal{M}$ quantifies the information leakage among the experts. We show that under some assumptions $\lambda(\pmb{\mu})$ is typically $\mathcal{O}(\log N)$. We implement our algorithm with stochastic experts generated from cost-sensitive classification oracles and show superior empirical performance on real-world datasets, when compared to other state of the art contextual bandit algorithms.

Exploratory analysis over network data is often limited by our ability to efficiently calculate graph statistics, which can provide a model-free understanding of macroscopic properties of a network. This work introduces a framework for estimating the graphlet count - the number of occurrences of a small subgraph motif (e.g. a wedge or a triangle) in the network. For massive graphs, where accessing the whole graph is not possible, the only viable algorithms are those which act locally by making a limited number of vertex neighborhood queries. We introduce a Monte Carlo sampling technique for graphlet counts, called lifting, which can simultaneously sample all graphlets of size up to $k$ vertices. We outline three variants of lifted graphlet counts: the ordered, unordered, and shotgun estimators. We prove that our graphlet count updates are unbiased for the true graphlet count, have low correlation between samples, and have a controlled variance. We compare the experimental performance of lifted graphlet counts to the state-of-the art graphlet sampling procedures: Waddling and the pairwise subgraph random walk.

We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint into the learning problem. It encourages the conditional risk of the learned classifier to be approximately constant with respect to the sensitive variable. We derive both risk and fairness bounds that support the statistical consistency of our approach. We specify our approach to kernel methods and observe that the fairness requirement implies an orthogonality constraint which can be easily added to these methods. We further observe that for linear models the constraint translates into a simple data preprocessing step. Experiments indicate that the method is empirically effective and performs favorably against state-of-the-art approaches.

We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks. Like the Kendall kernel, we show that the weighted version is invariant to relabeling of items and can be computed efficiently in $O(n \ln(n))$ operations, where $n$ is the number of items in the permutation. Second, we propose a supervised approach to learn the weights by jointly optimizing them with the function estimated by a kernel machine. Third, while the Kendall kernel considers pairwise comparison between items, we extend it by considering higher-order comparisons among tuples of items and show that the supervised approach of learning the weights can be systematically generalized to higher-order permutation kernels.

Determinantal point processes (DPPs) enable the modelling of repulsion: they provide diverse sets of points. This repulsion is encoded in a kernel K that we can see as a matrix storing the similarity between points. The usual algorithm to sample DPPs is exact but it uses the spectral decomposition of K, a computation that becomes costly when dealing with a high number of points. Here, we present an alternative exact algorithm that avoids the eigenvalues and the eigenvectors computation and that is, for some applications, faster than the original algorithm.

In recent works, both sparsity-based methods as well as learning-based methods have proven to be successful in solving several challenging linear inverse problems. However, sparsity priors for natural signals and images suffer from poor discriminative capability, while learning-based methods seldom provide concrete theoretical guarantees. In this work, we advocate the idea of replacing hand-crafted priors, such as sparsity, with a Generative Adversarial Network (GAN) to solve linear inverse problems such as compressive sensing. In particular, we propose a projected gradient descent (PGD) algorithm for effective use of GAN priors for linear inverse problems, and also provide theoretical guarantees on the rate of convergence of this algorithm. Moreover, we show empirically that our algorithm demonstrates superior performance over an existing method of leveraging GANs for compressive sensing.

We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihoods. The proposed method is recursive application of kernel ABC and kernel herding to the same observed data. We provide a theoretical explanation regarding why this approach works, showing (for the population setting) that the point estimate obtained with this method converges to the true parameter as recursion proceeds, under a certain assumption. We conduct a variety of numerical experiments, including parameter estimation for a real-world pedestrian flow simulator, and show that our method outperforms existing approaches in most cases.