Model selection, via penalized likelihood type criteria, is a standard task in many statistical inference and machine learning problems. Progress has led to deriving criteria with asymptotic consistency results and an increasing emphasis on introducing non-asymptotic criteria. We focus on the problem of modeling non-linear relationships in regression data with potential hidden graph-structured interactions between the high-dimensional predictors, within the mixture of experts modeling framework. In order to deal with such a complex situation, we investigate a block-diagonal localized mixture of polynomial experts (BLoMPE) regression model, which is constructed upon an inverse regression and block-diagonal structures of the Gaussian expert covariance matrices. We introduce a penalized maximum likelihood selection criterion to estimate the unknown conditional density of the regression model. This model selection criterion allows us to handle the challenging problem of inferring the number of mixture components, the degree of polynomial mean functions, and the hidden block-diagonal structures of the covariance matrices, which reduces the number of parameters to be estimated and leads to a trade-off between complexity and sparsity in the model. In particular, we provide a strong theoretical guarantee: a finite-sample oracle inequality satisfied by the penalized maximum likelihood estimator with a Jensen-Kullback-Leibler type loss, to support the introduced non-asymptotic model selection criterion. The penalty shape of this criterion depends on the complexity of the considered random subcollection of BLoMPE models, including the relevant graph structures, the degree of polynomial mean functions, and the number of mixture components.

A fundamental task in AI is to assess (in)dependence between mixed-type variables (text, image, sound). We propose a Bayesian kernelised correlation test of (in)dependence using a Dirichlet process model. The new measure of (in)dependence allows us to answer some fundamental questions: Based on data, are (mixed-type) variables independent? How likely is dependence/independence to hold? How high is the probability that two mixed-type variables are more than just weakly dependent? We theoretically show the properties of the approach, as well as algorithms for fast computation with it. We empirically demonstrate the effectiveness of the proposed method by analysing its performance and by comparing it with other frequentist and Bayesian approaches on a range of datasets and tasks with mixed-type variables.

Machine Learning services are being deployed in a large range of applications that make it easy for an adversary, using the algorithm and/or the model, to gain access to sensitive data. This paper investigates fundamental bounds on information leakage. First, we identify and bound the success rate of the worst-case membership inference attack, connecting it to the generalization error of the target model. Second, we study the question of how much sensitive information is stored by the algorithm about the training set and we derive bounds on the mutual information between the sensitive attributes and model parameters. Although our contributions are mostly of theoretical nature, the bounds and involved concepts are of practical relevance. Inspired by our theoretical analysis, we study linear regression and DNN models to illustrate how these bounds can be used to assess the privacy guarantees of ML models.

Hawkes Processes have undergone increasing popularity as default tools for modeling self- and mutually exciting interactions of discrete events in continuous-time event streams. A Maximum Likelihood Estimation (MLE) unconstrained optimization procedure over parametrically assumed forms of the triggering kernels of the corresponding intensity function are a widespread cost-effective modeling strategy, particularly suitable for data with few and/or short sequences. However, the MLE optimization lacks guarantees, except for strong assumptions on the parameters of the triggering kernels, and may lead to instability of the resulting parameters .In the present work, we show how a simple stabilization procedure improves the performance of the MLE optimization without these overly restrictive assumptions.This stabilized version of the MLE is shown to outperform traditional methods over sequences of several different lengths.

In order to develop reliable services using machine learning, it is important to understand the uncertainty of the model outputs. Often the probability distribution that the prediction target follows has a complex shape, and a mixture distribution is assumed as a distribution that uncertainty follows. Since the output of mixture density estimation is complicated, its interpretability becomes important when considering its use in real services. In this paper, we propose a method for mixture density estimation that utilizes an interpretable tree structure. Further, a fast inference procedure based on time-invariant information cache achieves both high speed and interpretability.

This is a course on Machine Learning, Deep Learning and Bayesian Learning (​yes all 3 topics in one place!!!). We start off by analysing data

An information cascade is a circumstance where agents make decisions in a sequential fashion by following other agents. Bikhchandani et al., predict that once a cascade starts it continues, even if it is wrong, until agents receive an external input such as public information. In an information cascade, even if an agent has its own personal choice, it is always overridden by observation of previous agents' actions. This could mean agents end up in a situation where they may act without valuing their own information. As information cascades can have serious social consequences, it is important to have a good understanding of what causes them. We present a detailed Bayesian model of the information gained by agents when observing the choices of other agents and their own private information. Compared to prior work, we remove the high impact of the first observed agent's action by incorporating a prior probability distribution over the information of unobserved agents and investigate an alternative model of choice to that considered in prior work: weighted random choice. Our results show that, in contrast to Bikhchandani's results, cascades will not necessarily occur and adding prior agents' information will delay the effects of cascades.

AI - Artificial Intelligence AGI - Artificial General Intelligence ANN - Artificial Neural Network ANOVA - Analysis of Variance ANT - Actor Network Theory API - Application Programming Interface APX - Amsterdam Power Exchange AVE - Average Variance Extracted BU - Business Unit CART - Classification and Regression Tree CBMV - Crowd-based Business Model Validation CR - Composite Reliability CT - Computed Tomography CVC - Corporate Venture Capital DR - Design Requirement DP - Design Principle DSR - Design Science Research DSS - Decision Support System EEX - European Energy Exchange FsQCA - Fuzzy-Set Qualitative Comparative Analysis GUI - Graphical User Interface HI-DSS - Hybrid Intelligence Decision Support System HIT - Human Intelligence Task IoT - Internet of Things IS - Information System IT - Information Technology MCC - Matthews Correlation Coefficient ML - Machine Learning OCT - Opportunity Creation Theory OGEMA 2.0 - Open Gateway Energy Management 2.0 OS - Operating System R&D - Research & Development RE - Renewable Energies RQ - Research Question SVM - Support Vector Machine SSD - Solid-State Drive SDK - Software Development Kit TCP/IP - Transmission Control Protocol/Internet Protocol TCT - Transaction Cost Theory UI - User Interface VaR - Value at Risk VC - Venture Capital VPP - Virtual Power Plant Chapter I

For Bayesian learning, given likelihood function and Gaussian prior, the elliptical slice sampler, introduced by Murray, Adams and MacKay 2010, provides a tool for the construction of a Markov chain for approximate sampling of the underlying posterior distribution. Besides of its wide applicability and simplicity its main feature is that no tuning is necessary. Under weak regularity assumptions on the posterior density we show that the corresponding Markov chain is geometrically ergodic and therefore yield qualitative convergence guarantees. We illustrate our result for Gaussian posteriors as they appear in Gaussian process regression, as well as in a setting of a multi-modal distribution. Remarkably, our numerical experiments indicate a dimension-independent performance of elliptical slice sampling even in situations where our ergodicity result does not apply.

Bayesian inference in generalized linear models (GLMs), i.e.~Gaussian regression with non-Gaussian likelihoods, is generally non-analytic and requires computationally expensive approximations, such as sampling or variational inference. We propose an approximate inference framework primarily designed to be computationally cheap while still achieving high approximation quality. The concept, which we call \emph{Laplace Matching}, involves closed-form, approximate, bi-directional transformations between the parameter spaces of exponential families. These are constructed from Laplace approximations under custom-designed basis transformations. The mappings can then be leveraged to effectively turn a latent Gaussian distribution into a conjugate prior for a rich class of observable variables. This effectively turns inference in GLMs into conjugate inference (with small approximation errors). We empirically evaluate the method in two different GLMs, showing approximation quality comparable to state-of-the-art approximate inference techniques at a drastic reduction in computational cost. More specifically, our method has a cost comparable to the \emph{very first} step of the iterative optimization usually employed in standard GLM inference.