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.

Alarm root cause analysis is a significant component in the day-to-day telecommunication network maintenance, and it is critical for efficient and accurate fault localization and failure recovery. In practice, accurate and self-adjustable alarm root cause analysis is a great challenge due to network complexity and vast amounts of alarms. A popular approach for failure root cause identification is to construct a graph with approximate edges, commonly based on either event co-occurrences or conditional independence tests. However, considerable expert knowledge is typically required for edge pruning. We propose a novel data-driven framework for root cause alarm localization, combining both causal inference and network embedding techniques. In this framework, we design a hybrid causal graph learning method (HPCI), which combines Hawkes Process with Conditional Independence tests, as well as propose a novel Causal Propagation-Based Embedding algorithm (CPBE) to infer edge weights. We subsequently discover root cause alarms in a real-time data stream by applying an influence maximization algorithm on the weighted graph. We evaluate our method on artificial data and real-world telecom data, showing a significant improvement over the best baselines.

There is a range of applications where the interest is in understanding interactions between a set of time series, including in neuroscience, genomics, econometrics, climate science, and social media analysis. For example, in neuroscience, one may seek to understand whether activity in one brain region correlates with later activity in another region, or to decipher instantaneous correlations between regions--both notions of functional connectivity. In genomics, there is an analogous study of gene regulatory networks. In econometrics, one may be interested in how various macroeconomic indicators predict one another. We also have unprecedented levels of data on people's actions--whether they be social media posts, purchase histories, or political voting records--and want to understand the dependencies between the actions of these individuals. Modern recording modalities and the ability to store and process large amounts of data have escalated the scale at which we seek to do such analyses. In many cases, one may seek notions of causal interactions amongst the time series, but be limited to drawing inferences from observational data without opportunities for experimentation and without known mechanistic models for the observed phenomena.

This paper produces an efficient Semidefinite Programming (SDP) solution for community detection that incorporates non-graph data, which in this context is known as side information. SDP is an efficient solution for standard community detection on graphs. We formulate a semi-definite relaxation for the maximum likelihood estimation of node labels, subject to observing both graph and non-graph data. This formulation is distinct from the SDP solution of standard community detection, but maintains its desirable properties. We calculate the exact recovery threshold for three types of non-graph information, which in this paper are called side information: partially revealed labels, noisy labels, as well as multiple observations (features) per node with arbitrary but finite cardinality. We find that SDP has the same exact recovery threshold in the presence of side information as maximum likelihood with side information. Thus, the methods developed herein are computationally efficient as well as asymptotically accurate for the solution of community detection in the presence of side information. Simulations show that the asymptotic results of this paper can also shed light on the performance of SDP for graphs of modest size.

Undirected graphical models have been widely used to model the conditional independence structure of high-dimensional random vector data for years. In many modern applications such as EEG and fMRI data, the observations are multivariate random functions rather than scalars. To model the conditional independence of this type of data, functional graphical models are proposed and have attracted an increasing attention in recent years. In this paper, we propose a neighborhood selection approach to estimate Gaussian functional graphical models. We first estimate the neighborhood of all nodes via function-on-function regression, and then we can recover the whole graph structure based on the neighborhood information. By estimating conditional structure directly, we can circumvent the need of a well-defined precision operator which generally does not exist. Besides, we can better explore the effect of the choice of function basis for dimension reduction. We give a criterion for choosing the best function basis and motivate two practically useful choices, which we justified by both theory and experiments and show that they are better than expanding each function onto its own FPCA basis as in previous literature. In addition, the neighborhood selection approach is computationally more efficient than fglasso as it is more easy to do parallel computing. The statistical consistency of our proposed methods in high-dimensional setting are supported by both theory and experiment.

We develop simple methods for constructing parameter priors for model choice among Directed Acyclic Graphical (DAG) models. In particular, we introduce several assumptions that permit the construction of parameter priors for a large number of DAG models from a small set of assessments. We then present a method for directly computing the marginal likelihood of every DAG model given a random sample with no missing observations. We apply this methodology to Gaussian DAG models which consist of a recursive set of linear regression models. We show that the only parameter prior for complete Gaussian DAG models that satisfies our assumptions is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let $W$ be an $n \times n$, $n \ge 3$, positive-definite symmetric matrix of random variables and $f(W)$ be a pdf of $W$. Then, f$(W)$ is a Wishart distribution if and only if $W_{11} - W_{12} W_{22}^{-1} W'_{12}$ is independent of $\{W_{12},W_{22}\}$ for every block partitioning $W_{11},W_{12}, W'_{12}, W_{22}$ of $W$. Similar characterizations of the normal and normal-Wishart distributions are provided as well.