These days we hear about machine learning and artificial intelligence (AI) in all aspects of life. We see machines that learn and imitate the human brain in order to automate human processes. There are autonomous cars that learn the road conditions to drive, personal assistants we can converse with and machines that can predict what stock markets will do. In some respects, it can appear as "magic." Behind machine learning there are some fundamental, well-studied and understood techniques.

As bonus, you also learn how to share your analysis results with your collegues friends and others and create visual analysis of your results. You will also have access to some practice questions, which will give you hand on experience.

The logarithm is an interesting character. Let us only understand its personality applicable for regression models. The fundamental property of a logarithm is its base. The typical base of the logarithm is 2, 10 or e. There is another common base for logarithms.

Raman spectroscopy is a ubiquitous method for characterisation of substances in a wide range of settings including industrial process control, planetary exploration, homeland security, life sciences, geological field expeditions and laboratory materials research. In all of these environments there is a requirement to identify substances from their Raman spectrum at high rates and often in high volumes. Whilst machine classification has been demonstrated to be an essential approach to achieve real time identification, it still requires preprocessing of the data. This is true regardless of whether peak detection or multivariate methods, operating on whole spectra, are used as input. A standard pipeline for a machine classification system based on Raman spectroscopy includes preprocessing in the following order: cosmic ray removal, smoothing and baseline correction.

We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that the observations do not reside on a regular grid, and the given order of the features is arbitrary and does not convey a notion of locality. Therefore, traditional transforms and metrics cannot be used for data organization and analysis. In this paper, our goal is to organize the data by defining an appropriate representation and metric such that they respect the smoothness and structure underlying the data. We also aim to generalize the joint clustering of observations and features in the case the data does not fall into clear disjoint groups. For this purpose, we propose multiscale data-driven transforms and metrics based on trees. Their construction is implemented in an iterative refinement procedure that exploits the co-dependencies between features and observations. Beyond the organization of a single dataset, our approach enables us to transfer the organization learned from one dataset to another and to integrate several datasets together. We present an application to breast cancer gene expression analysis: learning metrics on the genes to cluster the tumor samples into cancer sub-types and validating the joint organization of both the genes and the samples. We demonstrate that using our approach to combine information from multiple gene expression cohorts, acquired by different profiling technologies, improves the clustering of tumor samples.

The analysis of mixed data has been raising challenges in statistics and machine learning. One of two most prominent challenges is to develop new statistical techniques and methodologies to effectively handle mixed data by making the data less heterogeneous with minimum loss of information. The other challenge is that such methods must be able to apply in large-scale tasks when dealing with huge amount of mixed data. To tackle these challenges, we introduce parameter sharing and balancing extensions to our recent model, the mixed-variate restricted Boltzmann machine (MV.RBM) which can transform heterogeneous data into homogeneous representation. We also integrate structured sparsity and distance metric learning into RBM-based models. Our proposed methods are applied in various applications including latent patient profile modelling in medical data analysis and representation learning for image retrieval. The experimental results demonstrate the models perform better than baseline methods in medical data and outperform state-of-the-art rivals in image dataset.

In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks. We propose two algorithms which perform clustering on a number of small subgraphs and finally patches the results into a single clustering. The main advantage of these algorithms is that they bring down significantly the computational cost of traditional algorithms, including spectral clustering, semi-definite programs, modularity based methods, likelihood based methods etc., without losing on accuracy and even improving accuracy at times. These algorithms are also, by nature, parallelizable. Thus, exploiting the facts that most traditional algorithms are accurate and the corresponding optimization problems are much simpler in small problems, our divide-and-conquer methods provide an omnibus recipe for scaling traditional algorithms up to large networks. We prove consistency of these algorithms under various subgraph selection procedures and perform extensive simulations and real-data analysis to understand the advantages of the divide-and-conquer approach in various settings.

Revealing a community structure in a network or dataset is a central problem arising in many scientific areas. The modularity function $Q$ is an established measure quantifying the quality of a community, being identified as a set of nodes having high modularity. In our terminology, a set of nodes with positive modularity is called a \textit{module} and a set that maximizes $Q$ is thus called \textit{leading module}. Finding a leading module in a network is an important task, however the dimension of real-world problems makes the maximization of $Q$ unfeasible. This poses the need of approximation techniques which are typically based on a linear relaxation of $Q$, induced by the spectrum of the modularity matrix $M$. In this work we propose a nonlinear relaxation which is instead based on the spectrum of a nonlinear modularity operator $\mathcal M$. We show that extremal eigenvalues of $\mathcal M$ provide an exact relaxation of the modularity measure $Q$, however at the price of being more challenging to be computed than those of $M$. Thus we extend the work made on nonlinear Laplacians, by proposing a computational scheme, named \textit{generalized RatioDCA}, to address such extremal eigenvalues. We show monotonic ascent and convergence of the method. We finally apply the new method to several synthetic and real-world data sets, showing both effectiveness of the model and performance of the method.

Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their close connection to generalized linear models, it is also natural to incorporate covariate information in them. The current paper presents two universal fitting algorithms for networks with edge covariates: one based on nuclear norm penalization and the other based on projected gradient descent. Both algorithms are motivated by maximizing likelihood for a special class of inner-product models while working simultaneously for a wide range of different latent space models, such as distance models, which allow latent vectors to affect edge formation in flexible ways. These fitting methods, especially the one based on projected gradient descent, are fast and scalable to large networks. We obtain their rates of convergence for both inner-product models and beyond. The effectiveness of the modeling approach and fitting algorithms is demonstrated on five real world network datasets for different statistical tasks, including community detection with and without edge covariates, and network assisted learning.

Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also requires the storage of a large matrix in memory. These factors restrict the application of Gaussian Process regression to small and moderate size data sets. We present an algorithm that combines estimates from models developed using subsets of the data obtained in a manner similar to the bootstrap. The sample size is a critical parameter for this algorithm. Guidelines for reasonable choices of algorithm parameters, based on detailed experimental study, are provided. Various techniques have been proposed to scale Gaussian Processes to large scale regression tasks. The most appropriate choice depends on the problem context. The proposed method is most appropriate for problems where an additive model works well and the response depends on a small number of features. The minimax rate of convergence for such problems is attractive and we can build effective models with a small subset of the data. The Stochastic Variational Gaussian Process and the Sparse Gaussian Process are also appropriate choices for such problems. These methods pick a subset of data based on theoretical considerations. The proposed algorithm uses bagging and random sampling. Results from experiments conducted as part of this study indicate that the algorithm presented in this work can be as effective as these methods. Keywords: Big Data, Gaussian Process, Regression 2010 MSC: 00-01, 99-00 1. Introduction Gaussian Processes (GP) are attractive tools to perform supervised learning tasks on complex datasets on which traditional parametric methods may not be effective. They are also easier to use in comparison to alternatives like neural networks ([1]).