This paper studies the problem of post-hoc calibration of machine learning classifiers. We introduce the following desiderata for uncertainty calibration: (a) accuracy-preserving, (b) data-efficient, and (c) high expressive power. We show that none of the existing methods satisfy all three requirements, and demonstrate how Mix-n-Match calibration strategies (i.e., ensemble and composition) can help achieve remarkably better data-efficiency and expressive power while provably preserving classification accuracy of the original classifier. We also show that existing calibration error estimators (e.g., histogram-based ECE) are unreliable especially in small-data regime. Therefore, we propose an alternative data-efficient kernel density-based estimator for a reliable evaluation of the calibration performance and prove its asymptotically unbiasedness and consistency.

Data-driven sequential decision has found a wide range of applications in modern operations management, such as dynamic pricing, inventory control, and assortment optimization. Most existing research on data-driven sequential decision focuses on designing an online policy to maximize the revenue. However, the research on uncertainty quantification on the underlying true model function (e.g., demand function), a critical problem for practitioners, has not been well explored. In this paper, using the problem of demand function prediction in dynamic pricing as the motivating example, we study the problem of constructing accurate confidence intervals for the demand function. The main challenge is that sequentially collected data leads to significant distributional bias in the maximum likelihood estimator or the empirical risk minimization estimate, making classical statistics approaches such as the Wald's test no longer valid. We address this challenge by developing a debiased approach and provide the asymptotic normality guarantee of the debiased estimator. Based this the debiased estimator, we provide both point-wise and uniform confidence intervals of the demand function.

Hot stellar systems (HSS) are a collection of stars bound together by gravitational attraction. These systems hold clues to many mysteries of outer space so understanding their origin, evolution and physical properties is important but remains a huge challenge. We used multivariate $t$-mixtures model-based clustering to analyze 13456 hot stellar systems from Misgeld & Hilker (2011) that included 12763 candidate globular clusters and found eight homogeneous groups using the Bayesian Information Criterion (BIC). A nonparametric bootstrap procedure was used to estimate the confidence of each of our clustering assignments. The eight obtained groups can be characterized in terms of the correlation, mass, effective radius and surface density. Using conventional correlation-mass-effective radius-surface density notation, the largest group, Group 1, can be described as having positive-low-low-moderate characteristics. The other groups, numbered in decreasing sizes are similarly characterised, with Group 2 having positive-low-low-high characteristics, Group 3 displaying positive-low-low-moderate characteristics, Group 4 having positive-low-low-high characteristic, Group 5 displaying positive-low-moderate-moderate characteristic and Group 6 showing positive-moderate-low-high characteristic. The smallest group (Group 8) shows negative-low-moderate-moderate characteristic. Group 7 has no candidate clusters and so cannot be similarly labeled but the mass, effective radius correlation for these non-candidates indicates that they zare larger than typical globular clusters. Assertions drawn for each group are ambiguous for a few HSS having low confidence in classification. Our analysis identifies distinct kinds of HSS with varying confidence and provides novel insight into their physical and evolutionary properties.

Theoretical analysis of the divide-and-conquer based distributed learning with least square loss in the reproducing kernel Hilbert space (RKHS) have recently been explored within the framework of learning theory. However, the studies on learning theory for general loss functions and hypothesis spaces remain limited. To fill the gap, we study the risk performance of distributed empirical risk minimization (ERM) for general loss functions and hypothesis spaces. The main contributions are two-fold. First, we derive two tight risk bounds under certain basic assumptions on the hypothesis space, as well as the smoothness, Lipschitz continuity, strong convexity of the loss function. Second, we further develop a more general risk bound for distributed ERM without the restriction of strong convexity.

Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributions in order to implement the kernel Bayes rule and build sequential data models. It was recently shown that transfer operators such as the Perron-Frobenius or Koopman operator can also be approximated in a similar fashion using covariance and cross-covariance operators and that eigenfunctions of these operators can be obtained by solving associated matrix eigenvalue problems. The goal of this paper is to provide a solid functional analytic foundation for the eigenvalue decomposition of RKHS operators and to extend the approach to the singular value decomposition. The results are illustrated with simple guiding examples.

Cognitive impairment has become epidemic in older adult population. The recent advent of tiny wearable and ambient devices, a.k.a Internet of Things (IoT) provides ample platforms for continuous functional and cognitive health assessment of older adults. In this paper, we design, implement and evaluate AutoCogniSys, a context-aware automated cognitive health assessment system, combining the sensing powers of wearable physiological (Electrodermal Activity, Photoplethysmography) and physical (Accelerometer, Object) sensors in conjunction with ambient sensors. We design appropriate signal processing and machine learning techniques, and develop an automatic cognitive health assessment system in a natural older adults living environment. We validate our approaches using two datasets: (i) a naturalistic sensor data streams related to Activities of Daily Living and mental arousal of 22 older adults recruited in a retirement community center, individually living in their own apartments using a customized inexpensive IoT system (IRB #HP-00064387) and (ii) a publicly available dataset for emotion detection. The performance of AutoCogniSys attests max. 93\% of accuracy in assessing cognitive health of older adults.

In this paper, we solve the problem of predicting the next locations of the moving objects with a historical dataset of trajectories. We present a Next Location Predictor with Markov Modeling (NLPMM) which has the following advantages: (1) it considers both individual and collective movement patterns in making prediction, (2) it is effective even when the trajectory data is sparse, (3) it considers the time factor and builds models that are suited to different time periods. We have conducted extensive experiments in a real dataset, and the results demonstrate the superiority of NLPMM over existing methods.

L1 and L2 regularisation owes its name to L1 and L2 norm of a vector w respectively. A linear regression model that implements L1 norm for regularisation is called lasso regression, and one that implements (squared) L2 norm for regularisation is called ridge regression. Note: Strictly speaking, the last equation (ridge regression) is a loss function with squared L2 norm of the weights (notice the absence of the square root). The regularisation terms are'constraints' by which an optimisation algorithm must'adhere to' when minimising the loss function, apart from having to minimise the error between the true y and the predicted ŷ. Let's define a model to see how L1 and L2 work.

Automated tuning of compute kernels is a popular area of research, mainly focused on finding optimal kernel parameters for a problem with fixed input sizes. This approach is good for deploying machine learning models, where the network topology is constant, but machine learning research often involves changing network topologies and hyperparameters. Traditional kernel auto-tuning has limited impact in this case; a more general selection of kernels is required for libraries to accelerate machine learning research. In this paper we present initial results using machine learning to select kernels in a case study deploying high performance SYCL kernels in libraries that target a range of heterogeneous devices from desktop GPUs to embedded accelerators. The techniques investigated apply more generally and could similarly be integrated with other heterogeneous programming systems. By combining auto-tuning and machine learning these kernel selection processes can be deployed with little developer effort to achieve high performance on new hardware.

The problem of identifying change points in high-dimensional Gaussian graphical models (GGMs) in an online fashion is of interest, due to new applications in biology, economics and social sciences. The offline version of the problem, where all the data are a priori available, has led to a number of methods and associated algorithms involving regularized loss functions. However, for the online version, there is currently only a single work in the literature that develops a sequential testing procedure and also studies its asymptotic false alarm probability and power. The latter test is best suited for the detection of change points driven by global changes in the structure of the precision matrix of the GGM, in the sense that many edges are involved. Nevertheless, in many practical settings the change point is driven by local changes, in the sense that only a small number of edges exhibit changes. To that end, we develop a novel test to address this problem that is based on the $\ell_\infty$ norm of the normalized covariance matrix of an appropriately selected portion of incoming data. The study of the asymptotic distribution of the proposed test statistic under the null (no presence of a change point) and the alternative (presence of a change point) hypotheses requires new technical tools that examine maxima of graph-dependent Gaussian random variables, and that of independent interest. It is further shown that these tools lead to the imposition of mild regularity conditions for key model parameters, instead of more stringent ones required by leveraging previously used tools in related problems in the literature. Numerical work on synthetic data illustrates the good performance of the proposed detection procedure both in terms of computational and statistical efficiency across numerous experimental settings.