We present a data-driven framework for incorporating side information in dynamic optimization under uncertainty. Specifically, our approach uses predictive machine learning methods (such as k-nearest neighbors, kernel regression, and random forests) to weight the relative importance of various data-driven uncertainty sets in a robust optimization formulation. Through a novel measure concentration result for local machine learning methods, we prove that the proposed framework is asymptotically optimal for stochastic dynamic optimization with covariates. We also describe a general-purpose approximation for the proposed framework, based on overlapping linear decision rules, which is computationally tractable and produces high-quality solutions for dynamic problems with many stages. Across a variety of examples in shipment planning, inventory management, and finance, our method achieves improvements of up to 15% over alternatives and requires less than one minute of computation time on problems with twelve stages.

Privacy has raised considerable concerns recently, especially with the advent of information explosion and numerous data mining techniques to explore the information inside large volumes of data. In this context, a new distributed learning paradigm termed federated learning becomes prominent recently to tackle the privacy issues in distributed learning, where only learning models will be transmitted from the distributed nodes to servers without revealing users' own data and hence protecting the privacy of users. In this paper, we propose a horizontal federated XGBoost algorithm to solve the federated anomaly detection problem, where the anomaly detection aims to identify abnormalities from extremely unbalanced datasets and can be considered as a special classification problem. Our proposed federated XGBoost algorithm incorporates data aggregation and sparse federated update processes to balance the tradeoff between privacy and learning performance. In particular, we introduce the virtual data sample by aggregating a group of users' data together at a single distributed node. We compute parameters based on these virtual data samples in the local nodes and aggregate the learning model in the central server. In the learning model upgrading process, we focus more on the wrongly classified data before in the virtual sample and hence to generate sparse learning model parameters. By carefully controlling the size of these groups of samples, we can achieve a tradeoff between privacy and learning performance. Our experimental results show the effectiveness of our proposed scheme by comparing with existing state-of-the-arts.

In stochastic gradient descent, especially for neural network training, there are currently dominating first order methods: not modeling local distance to minimum. This information required for optimal step size is provided by second order methods, however, they have many difficulties, starting with full Hessian having square of dimension number of coefficients. This article proposes a minimal step from successful first order momentum method toward second order: online parabola modelling in just a single direction: normalized $\hat{v}$ from momentum method. It is done by estimating linear trend of gradients $\vec{g}=\nabla F(\vec{\theta})$ in $\hat{v}$ direction: such that $g(\vec{\theta}_\bot+\theta\hat{v})\approx \lambda (\theta -p)$ for $\theta = \vec{\theta}\cdot \hat{v}$, $g= \vec{g}\cdot \hat{v}$, $\vec{\theta}_\bot=\vec{\theta}-\theta\hat{v}$. Using linear regression, $\lambda$, $p$ are MSE estimated by just updating four averages (of $g$, $\theta$, $g\theta$, $\theta^2$) in the considered direction. Exponential moving averages allow here for inexpensive online estimation, weakening contribution of the old gradients. Controlling sign of curvature $\lambda$, we can repel from saddles in contrast to attraction in standard Newton method. In the remaining directions: not considered in second order model, we can simultaneously perform e.g. gradient descent.

Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in general performing exact inference requires all of the data to be processed at each iteration of the algorithm. For large data sets, the computational cost of MCMC can be prohibitive, which has led to recent developments in scalable Monte Carlo algorithms that have a significantly lower computational cost than standard MCMC. In this paper, we focus on a particular class of scalable Monte Carlo algorithms, stochastic gradient Markov chain Monte Carlo (SGMCMC) which utilises data subsampling techniques to reduce the per-iteration cost of MCMC. We provide an introduction to some popular SGMCMC algorithms and review the supporting theoretical results, as well as comparing the efficiency of SGMCMC algorithms against MCMC on benchmark examples. The supporting R code is available online.

We study the center and median clustering problems for high-dimensional polygonal curves with finite but unbounded complexity. We tackle the computational issue that arises from the high number of dimensions by defining a Johnson-Lindenstrauss projection for polygonal curves. We analyze the resulting error in terms of the Fr\'echet distance, which is a natural dissimilarity measure for curves. Our algorithms for the median clustering achieve sublinear dependency on the number of input curves via subsampling. For the center clustering we utilize Buchin et al. (2019a) algorithm that achieves linear running-time in the number of input curves. We evaluate our results empirically utilizing a fast, CUDA-parallelized variant of the Alt and Godau algorithm for the Fr\'echet distance. Our experiments show that our clustering algorithms have fast and accurate practical implementations that yield meaningful results on real world data from various physical domains.

This work proposes the Bregman-Tweedie classification model and analyzes the domain structure of the extended exponential function, an extension of the classic generalized exponential function with additional scaling parameter, and related high-level mathematical structures, such as the Bregman-Tweedie loss function and the Bregman-Tweedie divergence. The base function of this divergence is the convex function of Legendre type induced from the extended exponential function. The Bregman-Tweedie loss function of the proposed classification model is the regular Legendre transformation of the Bregman-Tweedie divergence. This loss function is a polynomial parameterized function between unhinge loss and the logistic loss function. Actually, we have two sub-models of the Bregman-Tweedie classification model; H-Bregman with hinge-like loss function and L-Bregman with logisticlike loss function. Although the proposed classification model is nonconvex and unbounded, empirically, we have observed that the H-Bregman and L-Bregman outperform, in terms of the Friedman ranking, logistic regression and SVM and show reasonable performance in terms of the classification accuracy in the category of the binary linear classification problem. Keywords: Extended exponential function, convex function of Legendre type, Bregman-Tweedie divergence, Bregman-Tweedie classification model, hinge loss, logistic loss.

Risk adjustment has become an increasingly important tool in healthcare. It has been extensively applied to payment adjustment for health plans to reflect the expected cost of providing coverage for members. Risk adjustment models are typically estimated using linear regression, which does not fully exploit the information in claims data. Moreover, the development of such linear regression models requires substantial domain expert knowledge and computational effort for data preprocessing. In this paper, we propose a novel approach for risk adjustment that uses semantic embeddings to represent patient medical histories. Embeddings efficiently represent medical concepts learned from diagnostic, procedure, and prescription codes in patients' medical histories. This approach substantially reduces the need for feature engineering. Our results show that models using embeddings had better performance than a commercial risk adjustment model on the task of prospective risk score prediction.

Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand the dynamical features of the input driving time series that are formed in the state space. We propose a framework for rigorous analysis of such state representations in vanishing memory state space models such as echo state networks (ESN). In particular, we consider the state space a temporal feature space and the readout mapping from the state space a kernel machine operating in that feature space. We show that: (1) The usual ESN strategy of randomly generating input-to-state, as well as state coupling leads to shallow memory time series representations, corresponding to cross-correlation operator with fast exponentially decaying coefficients; (2) Imposing symmetry on dynamic coupling yields a constrained dynamic kernel matching the input time series with straightforward exponentially decaying motifs or exponentially decaying motifs of the highest frequency; (3) Simple cycle high-dimensional reservoir topology specified only through two free parameters can implement deep memory dynamic kernels with a rich variety of matching motifs. We quantify richness of feature representations imposed by dynamic kernels and demonstrate that for dynamic kernel associated with cycle reservoir topology, the kernel richness undergoes a phase transition close to the edge of stability.

In data mining, machine learning, and other areas of AI, we are often faced with datasets that contain many more attributes than needed, or that can even be helpful for tasks such as clustering or classification. Problems associated with such high dimensional data are for example the concentration effect of distances [13, 20] or irrelevant features [25, 49]. For clustering [31] and outlier detection [49], researchers have made use of various techniques to identify relevant subspaces, as defined by subsets of features that are informative for a particular task. Examples of how relevant subspaces can be determined for individual clusters or outliers include local density estimation in a systematic search through candidate subspaces (often following the Apriori principle [7] in various adaptations to the subspace search problem [48]), or the adaptation of distance measures based on the distribution within local neighborhoods (using some analysis of variance or even covariance -- typically based on PCA -- to allow also for an adaptation to correlated features). For sufficiently tight local neighborhoods, the underlying local data manifold can be regarded as approaching a linear form [40], an assumption that further justifies the determination of locally relevant features for subspace determination.

One of the challenges in display advertising is that the distribution of features and click through rate (CTR) can exhibit large shifts over time due to seasonality, changes to ad campaigns and other factors. The predominant strategy to keep up with these shifts is to train predictive models continuously, on fresh data, in order to prevent them from becoming stale. However, in many ad systems positive labels are only observed after a possibly long and random delay. These delayed labels pose a challenge to data freshness in continuous training: fresh data may not have complete label information at the time they are ingested by the training algorithm. Naive strategies which consider any data point a negative example until a positive label becomes available tend to underestimate CTR, resulting in inferior user experience and suboptimal performance for advertisers. The focus of this paper is to identify the best combination of loss functions and models that enable large-scale learning from a continuous stream of data in the presence of delayed labels. In this work, we compare 5 different loss functions, 3 of them applied to this problem for the first time. We benchmark their performance in offline settings on both public and proprietary datasets in conjunction with shallow and deep model architectures. We also discuss the engineering cost associated with implementing each loss function in a production environment. Finally, we carried out online experiments with the top performing methods, in order to validate their performance in a continuous training scheme. While training on 668 million in-house data points offline, our proposed methods outperform previous state-of-the-art by 3% relative cross entropy (RCE). During online experiments, we observed 55% gain in revenue per thousand requests (RPMq) against naive log loss.