I recently took Andrew Ng's Machine Learning course on Coursera, and I'm hoping to write a series of blog posts on what I learnt. In these we will look at a variety of machine learning techniques and categories, starting with linear and logistic regression. Machine learning is something of a buzzword at the moment, but underneath all the hype it's a technology that's expected to revolutionise virtually all industries, and have a huge impact on people's lives in the coming decades. Machine learning problems can be split into supervised learning and unsupervised learning. Supervised learning works by giving the algorithm the "right answers", which are used to train the algorithm so that it can fit and predict when given new examples.

Clustering is a Machine Learning technique that involves the grouping of data points. Given a set of data points, we can use a clustering algorithm to classify each data point into a specific group. In theory, data points that are in the same group should have similar properties and/or features, while data points in different groups should have highly dissimilar properties and/or features. Clustering is a method of unsupervised learning and is a common technique for statistical data analysis used in many fields. In Data Science, we can use clustering analysis to gain some valuable insights from our data by seeing what groups the data points fall into when we apply a clustering algorithm.

We perform unsupervised analysis of image-derived shape and motion features extracted from 3822 cardiac 4D MRIs of the UK Biobank. First, with a feature extraction method previously published based on deep learning models, we extract from each case 9 feature values characterizing both the cardiac shape and motion. Second, a feature selection is performed to remove highly correlated feature pairs. Third, clustering is carried out using a Gaussian mixture model on the selected features. After analysis, we identify two small clusters which probably correspond to two pathological categories. Further confirmation using a trained classification model and dimensionality reduction tools is carried out to support this discovery. Moreover, we examine the differences between the other large clusters and compare our measures with the ground-truth.

Abstract--The topological information is essential for studying the relationship between nodes in a network. Recently, Network Representation Learning (NRL), which projects a network into a low-dimensional vector space, has been shown their advantages inanalyzing large-scale networks. However, most existing NRL methods are designed to preserve the local topology of a network, they fail to capture the global topology. To tackle this issue, we propose a new NRL framework, named HSRL, to help existing NRL methods capture both the local and global topological information of a network. Then, an existing NRL method is used to learn node embeddings for each compressed network. Finally, the node embeddings of the input network are obtained by concatenating the node embeddings from all compressed networks. Empirical studies for link prediction on five real-world datasets demonstrate the advantages of HSRL over state-of-the-art methods. I. INTRODUCTION The science of networks has been widely used to understand thebehaviours of complex systems.

We consider learning two layer neural networks using stochastic gradient descent. The mean-field description of this learning dynamics approximates the evolution of the network weights by an evolution in the space of probability distributions in $R^D$ (where $D$ is the number of parameters associated to each neuron). This evolution can be defined through a partial differential equation or, equivalently, as the gradient flow in the Wasserstein space of probability distributions. Earlier work shows that (under some regularity assumptions), the mean field description is accurate as soon as the number of hidden units is much larger than the dimension $D$. In this paper we establish stronger and more general approximation guarantees. First of all, we show that the number of hidden units only needs to be larger than a quantity dependent on the regularity properties of the data, and independent of the dimensions. Next, we generalize this analysis to the case of unbounded activation functions, which was not covered by earlier bounds. We extend our results to noisy stochastic gradient descent. Finally, we show that kernel ridge regression can be recovered as a special limit of the mean field analysis.

The excluded area between a pair of two-dimensional hard particles with given relative orientation is the region in which one particle cannot be located due to the presence of the other particle. The magnitude of the excluded area as a function of the relative particle orientation plays a major role in the determination of the bulk phase behaviour of hard particles. We use principal component analysis to identify the different types of excluded area corresponding to randomly generated two-dimensional hard particles modeled as non-self-intersecting polygons and star lines (line segments radiating from a common origin). Only three principal components are required to have an excellent representation of the value of the excluded area as a function of the relative particle orientation. Independently of the particle shape, the minimum value of the excluded area is always achieved when the particles are antiparallel to each other. The property that affects the value of the excluded area most strongly is the elongation of the particle shape. Principal component analysis identifies four limiting cases of excluded areas with one to four global minima at equispaced relative orientations. We study selected particle shapes using Monte Carlo simulations.

Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve mixing/convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain Monte Carlo. Nonetheless, introducing appropriate auxiliary variables while preserving the initial target probability distribution cannot be conducted in a systematic way but highly depends on the considered problem. To deal with such issues, this paper draws a unified framework, namely asymptotically exact data augmentation (AXDA), which encompasses several well-established but also more recent approximate augmented models. Benefiting from a much more general perspective, it delivers some additional qualitative and quantitative insights concerning these schemes. In particular, general properties of AXDA along with non-asymptotic theoretical results on the approximation that is made are stated. Close connections to existing Bayesian methods (e.g. mixture modeling, robust Bayesian models and approximate Bayesian computation) are also drawn. All the results are illustrated with examples and applied to standard statistical learning problems.

The deep network model, with the majority built on neural networks, has been proved to be a powerful framework to represent complex data for high performance machine learning. In recent years, more and more studies turn to nonneural network approaches to build diverse deep structures, and the Deep Stacking Network (DSN) model is one of such approaches that uses stacked easy-to-learn blocks to build a parameter-training-parallelizable deep network. In this paper, we propose a novel SVM-based Deep Stacking Network (SVM-DSN), which uses the DSN architecture to organize linear SVM classifiers for deep learning. A BP-like layer tuning scheme is also proposed to ensure holistic and local optimizations of stacked SVMs simultaneously. Some good math properties of SVM, such as the convex optimization, is introduced into the DSN framework by our model. From a global view, SVM-DSN can iteratively extract data representations layer by layer as a deep neural network but with parallelizability, and from a local view, each stacked SVM can converge to its optimal solution and obtain the support vectors, which compared with neural networks could lead to interesting improvements in anti-saturation and interpretability. Experimental results on both image and text data sets demonstrate the excellent performances of SVM-DSN compared with some competitive benchmark models.

Empirical studies show that gradient based methods can learn deep neural networks (DNNs) with very good generalization performance in the over-parameterization regime, where DNNs can easily fit a random labeling of the training data. While a line of recent work explains in theory that gradient-based methods with proper random initialization can find the global minima of the training loss in over-parameterized DNNs, it does not explain the good generalization performance of the gradient-based methods for learning over-parameterized DNNs. In this work, we take a step further, and prove that under certain assumption on the data distribution that is milder than linear separability, gradient descent (GD) with proper random initialization is able to train a sufficiently over-parameterized DNN to achieve arbitrarily small expected error (i.e., population error). This leads to an algorithmic-dependent generalization error bound for deep learning. To the best of our knowledge, this is the first result of its kind that can explain the good generalization performance of over-parameterized deep neural networks learned by gradient descent.

Time series analysis is the use of statistical methods to analyze time series data and extract meaningful statistics and characteristics of the data. In this blog, we will begin our journey of learning time series forecasting using python. We will be taking a small forecasting problem and try to solve it till the end learning time series forecasting alongside. Time series analysis is the collection of data at specific intervals over a period of time, with the purpose of identifying trends, cycles, and seasonal variances to aid in the forecasting of a future event. Data is any observed outcome that's measurable. Unlike in statistical sampling, in time series analysis, data must be measured over time at consistent intervals to identify patterns that form trends, cycles, and seasonal variances. Measurements at random intervals lose the ability to predict future events.