ABSTRACT We study the relationship between online Gaussian process (GP) regression and kernel least mean squares (KLMS) algorithms. While the latter have no capacity of storing the entire posterior distribution during online learning, we discover that their operation corresponds to the assumption of a fixed posterior covariance that follows a simple parametric model. Interestingly, several well-known KLMS algorithms correspond to specific cases of this model. The probabilistic perspective allows us to understand how each of them handles uncertainty, which could explain some of their performance differences. Index Terms-- online learning, regression, Gaussian processes, kernel least-mean squares 1. INTRODUCTION Gaussian Process (GP) regression is a state-of-the-art Bayesian technique for nonlinear regression [1].

Singularities of a statistical model are the elements of the model's parameter space which make the corresponding Fisher information matrix degenerate. These are the points for which estimation techniques such as the maximum likelihood estimator and standard Bayesian procedures do not admit the root-$n$ parametric rate of convergence. We propose a general framework for the identification of singularity structures of the parameter space of finite mixtures, and study the impacts of the singularity levels on minimax lower bounds and rates of convergence for the maximum likelihood estimator over a compact parameter space. Our study makes explicit the deep links between model singularities, parameter estimation convergence rates and minimax lower bounds, and the algebraic geometry of the parameter space for mixtures of continuous distributions. The theory is applied to establish concrete convergence rates of parameter estimation for finite mixture of skewnormal distributions. This rich and increasingly popular mixture model is shown to exhibit a remarkably complex range of asymptotic behaviors which have not been hitherto reported in the literature.

The Predictive Analytics Scores below – ordered on Forecasted Future Needs and Demand from High to Low – shows you Machine learning's Predictive Analysis. The link takes you to a corresponding product in The Art of Service's store to get started. The Art of Service's predictive model results enable businesses to discover and apply the most profitable technologies and applications, attracting the most profitable customers, and therefore helping maximize value from their investments. The Predictive Analytics algorithm evaluates and scores technologies and applications. The platform monitors over six thousand technologies and applications for months, looking for interest swings in a topic, concept, technology or application, not just a count of mentions.

Although there has been substantial research in software analytics for effort estimation in traditional software projects, little work has been done for estimation in agile projects, especially estimating user stories or issues. Story points are the most common unit of measure used for estimating the effort involved in implementing a user story or resolving an issue. In this paper, we offer for the \emph{first} time a comprehensive dataset for story points-based estimation that contains 23,313 issues from 16 open source projects. We also propose a prediction model for estimating story points based on a novel combination of two powerful deep learning architectures: long short-term memory and recurrent highway network. Our prediction system is \emph{end-to-end} trainable from raw input data to prediction outcomes without any manual feature engineering. An empirical evaluation demonstrates that our approach consistently outperforms three common effort estimation baselines and two alternatives in both Mean Absolute Error and the Standardized Accuracy.

Hearing Aid (HA) algorithms need to be tuned ("fitted") to match the impairment of each specific patient. The lack of a fundamental HA fitting theory is a strong contributing factor to an unsatisfying sound experience for about 20% of hearing aid patients. This paper proposes a probabilistic modeling approach to the design of HA algorithms. The proposed method relies on a generative probabilistic model for the hearing loss problem and provides for automated inference of the corresponding (1) signal processing algorithm, (2) the fitting solution as well as a principled (3) performance evaluation metric. All three tasks are realized as message passing algorithms in a factor graph representation of the generative model, which in principle allows for fast implementation on hearing aid or mobile device hardware. The methods are theoretically worked out and simulated with a custom-built factor graph toolbox for a specific hearing loss model.

Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case basis; examples include robust linear regression, robust mixture models, and bursty topic models. In this paper we develop a general approach to robust Bayesian modeling. We show how to turn an existing Bayesian model into a robust model, and then develop a generic strategy for computing with it. We use our method to study robust variants of several models, including linear regression, Poisson regression, logistic regression, and probabilistic topic models. We discuss the connections between our methods and existing approaches, especially empirical Bayes and James-Stein estimation.

We address the task of simultaneous feature fusion and modeling of discrete ordinal outputs. We propose a novel Gaussian process(GP) auto-encoder modeling approach. In particular, we introduce GP encoders to project multiple observed features onto a latent space, while GP decoders are responsible for reconstructing the original features. Inference is performed in a novel variational framework, where the recovered latent representations are further constrained by the ordinal output labels. In this way, we seamlessly integrate the ordinal structure in the learned manifold, while attaining robust fusion of the input features. We demonstrate the representation abilities of our model on benchmark datasets from machine learning and affect analysis. We further evaluate the model on the tasks of feature fusion and joint ordinal prediction of facial action units. Our experiments demonstrate the benefits of the proposed approach compared to the state of the art.

While perception tasks such as visual object recognition and text understanding play an important role in human intelligence, the subsequent tasks that involve inference, reasoning and planning require an even higher level of intelligence. The past few years have seen major advances in many perception tasks using deep learning models. For higher-level inference, however, probabilistic graphical models with their Bayesian nature are still more powerful and flexible. To achieve integrated intelligence that involves both perception and inference, it is naturally desirable to tightly integrate deep learning and Bayesian models within a principled probabilistic framework, which we call Bayesian deep learning. In this unified framework, the perception of text or images using deep learning can boost the performance of higher-level inference and in return, the feedback from the inference process is able to enhance the perception of text or images. This paper proposes a general framework for Bayesian deep learning and reviews its recent applications on recommender systems, topic models, and control. In this paper, we also discuss the relationship and differences between Bayesian deep learning and other related topics like Bayesian treatment of neural networks.

In most classification tasks there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classification allows the classifiers to output a set of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framework for multiclass set-valued classification, where the classifiers guarantee user-defined levels of coverage or confidence (the probability that the true label is contained in the set) while minimizing the ambiguity (the expected size of the output). We first derive oracle classifiers assuming the true distribution to be known. We show that the oracle classifiers are obtained from level sets of the functions that define the conditional probability of each class. Then we develop estimators with good asymptotic and finite sample properties. The proposed classifiers build on and refine many existing single-label classifiers. The optimal classifier can sometimes output the empty set. We provide two solutions to fix this issue that are suitable for various practical needs.

The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-$\ell_1$-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection and prediction properties, as well as minimax optimality. This paper introduces the Bayesian SLOPE procedure for linear regression. The classical SLOPE estimate is the posterior mode in the normal regression problem with an appropriate prior on the coefficients. The Bayesian SLOPE considers the full Bayesian model and has the advantage of offering credible sets and standard error estimates for the parameters. Moreover, the hierarchical Bayesian framework allows for full Bayesian and empirical Bayes treatment of the penalty coefficients; whereas it is not clear how to choose these coefficients when using the SLOPE on a general design matrix. A direct characterization of the posterior is provided which suggests a Gibbs sampler that does not involve latent variables. An efficient hybrid Gibbs sampler for the Bayesian SLOPE is introduced. Point estimation using the posterior mean is highlighted, which automatically facilitates the Bayesian prediction of future observations. These are demonstrated on real and synthetic data.