Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and simultaneous Bayesian credible sets in GP regression. As an intermediate result, we develop a Bernstein von-Mises type result under supremum norm in random design GP regression. Identifying both the mean and covariance function of the posterior distribution of the Gaussian process as regularized $M$-estimators, we show that the sampling distribution of the posterior mean function and the centered posterior distribution can be respectively approximated by two population level GPs. By developing a comparison inequality between two GPs, we provide exact characterization of frequentist coverage probabilities of Bayesian point-wise credible intervals and simultaneous credible bands of the regression function. Our results show that inference based on GP regression tends to be conservative; when the prior is under-smoothed, the resulting credible intervals and bands have minimax-optimal sizes, with their frequentist coverage converging to a non-degenerate value between their nominal level and one. As a byproduct of our theory, we show that the GP regression also yields minimax-optimal posterior contraction rate relative to the supremum norm, which provides a positive evidence to the long standing problem on optimal supremum norm contraction rate in GP regression.

Missing data and noisy observations pose significant challenges for reliably predicting events from irregularly sampled multivariate time series (longitudinal) data. Imputation methods, which are typically used for completing the data prior to event prediction, lack a principled mechanism to account for the uncertainty due to missingness. Alternatively, state-of-the-art joint modeling techniques can be used for jointly modeling the longitudinal and event data and compute event probabilities conditioned on the longitudinal observations. These approaches, however, make strong parametric assumptions and do not easily scale to multivariate signals with many observations. Our proposed approach consists of several key innovations. First, we develop a flexible and scalable joint model based upon sparse multiple-output Gaussian processes. Unlike state-of-the-art joint models, the proposed model can explain highly challenging structure including non-Gaussian noise while scaling to large data. Second, we derive an optimal policy for predicting events using the distribution of the event occurrence estimated by the joint model. The derived policy trades-off the cost of a delayed detection versus incorrect assessments and abstains from making decisions when the estimated event probability does not satisfy the derived confidence criteria. Experiments on a large dataset show that the proposed framework significantly outperforms state-of-the-art techniques in event prediction.

Disagreement-based approaches generate multiple classifiers and exploit the disagreement among them with unlabeled data to improve learning performance. Co-training is a representative paradigm of them, which trains two classifiers separately on two sufficient and redundant views; while for the applications where there is only one view, several successful variants of co-training with two different classifiers on single-view data instead of two views have been proposed. For these disagreement-based approaches, there are several important issues which still are unsolved, in this article we present theoretical analyses to address these issues, which provides a theoretical foundation of co-training and disagreement-based approaches. Keywords: machine learning, semi-supervised learning, disagreement-based learning, co-training, multi-view classification, combination 1. Introduction Learning from labeled training data is well-established in traditional machine learning, but labeling the data is time-consuming, sometimes may be very expensive since it requires human efforts. In many practical applications, unlabeled data can be obtained abundantly and cheaply.

Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in machine learning for massive data sets (big data). In particular, stochastic gradient methods are considered the de- facto standard for training deep neural networks. Studying gradient methods within the realm of fixed-point theory provides us with powerful tools to analyze their convergence properties. In particular, gradient methods using inexact or noisy gradients, such as stochastic gradient descent, can be studied conveniently using well-known results on inexact fixed-point iterations. Moreover, as we demonstrate in this paper, the fixed-point approach allows an elegant derivation of accelerations for basic gradient methods. In particular, we will show how gradient descent can be accelerated by a fixed-point preserving transformation of an operator associated with the objective function.

Abstract: Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical covariance estimator, and its modifications, is very sensitive to the presence of outliers in the data. As P. Huber wrote [Hub64], "...This raises a question which could have been asked already by Gauss, but which was, as far as I know, only raised a few years ago (notably by Tukey): what happens if the true distribution deviates slightly from the assumed normal one? As is now well known, the sample mean then may have a catastrophically bad performance..." Motivated by Tukey's question, we develop a new estimator of the (element-wise) mean of a random matrix, which includes covariance estimation problem as a special case. Assuming that the entries of a matrix possess only finite second moment, this new estimator admits sub-Gaussian or subexponential concentration around the unknown mean in the operator norm. We explain the key ideas behind our construction, and discuss applications to covariance estimation and matrix completion problems.

There has been a growing interest in using nonparametric regression methods like Gaussian Process (GP) regression for system identification. GP regression does traditionally have three important downsides: (1) it is computationally intensive, (2) it cannot efficiently implement newly obtained measurements online, and (3) it cannot deal with stochastic (noisy) input points. In this paper we present an algorithm tackling all these three issues simultaneously. The resulting Sparse Online Noisy Input GP (SONIG) regression algorithm can incorporate new noisy measurements in constant runtime. A comparison has shown that it is more accurate than similar existing regression algorithms. When applied to nonlinear black-box system modeling, its performance is competitive with existing nonlinear ARX models. Keywords: Nonlinear system identification, Gaussian processes, regression, machine learning, sparse methods.

Topic models, and more specifically the class of Latent Dirichlet Allocation (LDA), are widely used for probabilistic modeling of text. MCMC sampling from the posterior distribution is typically performed using a collapsed Gibbs sampler. We propose a parallel sparse partially collapsed Gibbs sampler and compare its speed and efficiency to state-of-the-art samplers for topic models on five well-known text corpora of differing sizes and properties. In particular, we propose and compare two different strategies for sampling the parameter block with latent topic indicators. The experiments show that the increase in statistical inefficiency from only partial collapsing is smaller than commonly assumed, and can be more than compensated by the speedup from parallelization and sparsity on larger corpora. We also prove that the partially collapsed samplers scale well with the size of the corpus. The proposed algorithm is fast, efficient, exact, and can be used in more modeling situations than the ordinary collapsed sampler.

Accurately predicting the time of occurrence of an event of interest is a critical problem in longitudinal data analysis. One of the main challenges in this context is the presence of instances whose event outcomes become unobservable after a certain time point or when some instances do not experience any event during the monitoring period. Such a phenomenon is called censoring which can be effectively handled using survival analysis techniques. Traditionally, statistical approaches have been widely developed in the literature to overcome this censoring issue. In addition, many machine learning algorithms are adapted to effectively handle survival data and tackle other challenging problems that arise in real-world data. In this survey, we provide a comprehensive and structured review of the representative statistical methods along with the machine learning techniques used in survival analysis and provide a detailed taxonomy of the existing methods. We also discuss several topics that are closely related to survival analysis and illustrate several successful applications in various real-world application domains. We hope that this paper will provide a more thorough understanding of the recent advances in survival analysis and offer some guidelines on applying these approaches to solve new problems that arise in applications with censored data.

The Aim of the Conference The aim of the conference is to bring together researchers from all over the world who deal with machine learning and data mining in order to discuss the recent status of the research and to direct further developments. Basic research papers as well as application papers are welcome. Paper submissions should be related but not limited to any of the following topics: association rules case-based reasoning and learning classification and interpretation of images, text, video conceptional learning and clustering Goodness measures and evaluaion (e.g. Long Paper The paper must be formatted in the Springer LNCS format. They should have at most 15 pages.

Hello, This is my project on implementing some useful algorithm on excel. To my knowledge there is not any open source excel vba available till now. I found that unsupervised learning is probably more useful for excel context. Therefore, I am playing to implement EM algorithm next along of some other row reduction, factor analysis models. I think ANN, CNN and RNN will come eventually, but going to take quite some time. Implementing ML algorithm is just not a very present job using VBA lol.