Then this course is for you! This course has been designed by experts so that we can share our knowledge and help you learn complex theory, algorithms and coding libraries in a simple way. We will walk you step-by-step into the World of Machine Learning. With every tutorial you will develop new skills and improve your understanding of this challenging yet lucrative field of ML. This course is fun and exciting, but at the same time we dive deep into Machine Learning.

Importance-weighting is a popular and well-researched technique for dealing with sample selection bias and covariate shift. It has desirable characteristics such as unbiasedness, consistency and low computational complexity. However, weighting can have a detrimental effect on an estimator as well. In this work, we empirically show that the sampling distribution of an importance-weighted estimator can be skewed. For sample selection bias settings, and for small sample sizes, the importance-weighted risk estimator produces overestimates for datasets in the body of the sampling distribution, i.e. the majority of cases, and large underestimates for data sets in the tail of the sampling distribution. These over- and underestimates of the risk lead to suboptimal regularization parameters when used for importance-weighted validation.

The family of image visibility graphs (IVGs) have been recently introduced as simple algorithms by which scalar fields can be mapped into graphs. Here we explore the usefulness of such operator in the scenario of image processing and image classification. We demonstrate that the link architecture of the image visibility graphs encapsulates relevant information on the structure of the images and we explore their potential as image filters and compressors. We introduce several graph features, including the novel concept of Visibility Patches, and show through several examples that these features are highly informative, computationally efficient and universally applicable for general pattern recognition and image classification tasks.

This article describes the R package varrank. It has a flexible implementation of heuristic approaches which perform variable ranking based on mutual information. The package is particularly suitable for exploring multivariate datasets requiring a holistic analysis. The core functionality is a general implementation of the minimum redundancy maximum relevance (mRMRe) model. This approach is based on information theory metrics. It is compatible with discrete and continuous data which are discretised using a large choice of possible rules. The two main problems that can be addressed by this package are the selection of the most representative variables for modeling a collection of variables of interest, i.e., dimension reduction, and variable ranking with respect to a set of variables of interest.

Real-world networks such as social and communication networks are too large to be observed entirely. Such networks are often partially observed such that network size, network topology, and nodes of the original network are unknown. In this paper we formalize the Adaptive Graph Exploring problem. We assume that we are given an incomplete snapshot of a large network and additional nodes can be discovered by querying nodes in the currently observed network. The goal of this problem is to maximize the number of observed nodes within a given query budget. Querying which set of nodes maximizes the size of the observed network? We formulate this problem as an exploration-exploitation problem and propose a novel nonparametric multi-arm bandit (MAB) algorithm for identifying which nodes to be queried. Our contributions include: (1) $i$KNN-UCB, a novel nonparametric MAB algorithm, applies $k$-nearest neighbor UCB to the setting when the arms are presented in a vector space, (2) provide theoretical guarantee that $i$KNN-UCB algorithm has sublinear regret, and (3) applying $i$KNN-UCB algorithm on synthetic networks and real-world networks from different domains, we show that our method discovers up to 40% more nodes compared to existing baselines.

Gibbs sampling, as a model learning method, is known to produce the most accurate results available in a variety of domains, and is a de facto standard in these domains. Yet, it is also well known that Gibbs random walks usually have bottlenecks, sometimes termed "local maxima", and thus samplers often return suboptimal solutions. In this paper we introduce a variation of the Gibbs sampler which yields high likelihood solutions significantly more often than the regular Gibbs sampler. Specifically, we show that combining multiple samplers, with certain dependence (coupling) between them, results in higher likelihood solutions. This side-steps the well known issue of identifiability, which has been the obstacle to combining samplers in previous work. We evaluate the approach on a Latent Dirichlet Allocation model, and also on HMM's, where precise computation of likelihoods and comparisons to the standard EM algorithm are possible.

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the first kernel-based variable selection method applicable to large datasets. It sidesteps the typical poor scaling properties of kernel methods by mapping the inputs into a relatively low-dimensional space of random features. The algorithm discovers the variables relevant for the regression task together with learning the prediction model through learning the appropriate nonlinear random feature maps. We demonstrate the outstanding performance of our method on a set of large-scale synthetic and real datasets.

We describe two applications of machine learning in the context of IP/Optical networks. The first one allows agile management of resources at a core IP/Optical network by using machine learning for short-term and long-term prediction of traffic flows and joint global optimization of IP and optical layers using colorless/directionless (CD) flexible ROADMs. Multilayer coordination allows for significant cost savings, flexible new services to meet dynamic capacity needs, and improved robustness by being able to proactively adapt to new traffic patterns and network conditions. The second application is important as we migrate our metro networks to Open ROADM networks, to allow physical routing without the need for detailed knowledge of optical parameters. We discuss a proof-of-concept study, where detailed performance data for wavelengths on a current flexible ROADM network is used for machine learning to predict the optical performance of each wavelength. Both applications can be efficiently implemented by using a SDN (Software Defined Network) controller.

We show a sufficient condition on the dissimilarity measure that leads to the consistency of the algorithms for clustering offline and online data settings, respectively. As an example of application, clustering synthetic data sampled from multifractional Brownian motions is provided.

Let $X=\mathbf{X}\cup\mathbf{Z}$ be a data set in $\mathbb{R}^D$, where $\mathbf{X}$ is the training set and $\mathbf{Z}$ is the test one. Many unsupervised learning algorithms based on kernel methods have been developed to provide dimensionality reduction (DR) embedding for a given training set $\Phi: \mathbf{X} \to \mathbb{R}^d$ ( $d\ll D$) that maps the high-dimensional data $\mathbf{X}$ to its low-dimensional feature representation $\mathbf{Y}=\Phi(\mathbf{X})$. However, these algorithms do not straightforwardly produce DR of the test set $\mathbf{Z}$. An out-of-sample extension method provides DR of $\mathbf{Z}$ using an extension of the existent embedding $\Phi$, instead of re-computing the DR embedding for the whole set $X$. Among various out-of-sample DR extension methods, those based on Nystr\"{o}m approximation are very attractive. Many papers have developed such out-of-extension algorithms and shown their validity by numerical experiments. However, the mathematical theory for the DR extension still need further consideration. Utilizing the reproducing kernel Hilbert space (RKHS) theory, this paper develops a preliminary mathematical analysis on the out-of-sample DR extension operators. It treats an out-of-sample DR extension operator as an extension of the identity on the RKHS defined on $\mathbf{X}$. Then the Nystr\"{o}m-type DR extension turns out to be an orthogonal projection. In the paper, we also present the conditions for the exact DR extension and give the estimate for the error of the extension.