A representer theorem for deep kernel learning

In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for the analysis of machine learning algorithms based on compositions of functions. As a direct consequence in the finite-sample case, the corresponding infinite-dimensional minimization problems can be recast into (nonlinear) finite-dimensional minimization problems, which can be tackled with nonlinear optimization algorithms. Moreover, we show how concatenated machine learning problems can be reformulated as neural networks and how our representer theorem applies to a broad class of state-of-the-art deep learning methods

Analyzing sparse dictionaries for online learning with kernels

Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines, with new challenges emerging in online learning with kernels. To this end, several sparsity measures have been proposed in the literature to quantify sparse dictionaries and constructing relevant ones, the most prolific ones being the distance, the approximation, the coherence and the Babel measures. In this paper, we analyze sparse dictionaries based on these measures. By conducting an eigenvalue analysis, we show that these sparsity measures share many properties, including the linear independence condition and inducing a well-posed optimization problem. Furthermore, we prove that there exists a quasi-isometry between the parameter (i.e., dual) space and the dictionary's induced feature space.Comment: 10 page

Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these conditions, though weight sharing is not the main reason for their exponential advantage

Machine Learning of Molecular Electronic Properties in Chemical Compound Space

The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property relationships. Such relationships enable high-throughput screening for relevant properties in an exponentially growing pool of virtual compounds that are synthetically accessible. Here, we present a machine learning (ML) model, trained on a data base of \textit{ab initio} calculation results for thousands of organic molecules, that simultaneously predicts multiple electronic ground- and excited-state properties. The properties include atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity, and excitation energies. The ML model is based on a deep multi-task artificial neural network, exploiting underlying correlations between various molecular properties. The input is identical to \emph{ab initio} methods, \emph{i.e.} nuclear charges and Cartesian coordinates of all atoms. For small organic molecules the accuracy of such a "Quantum Machine" is similar, and sometimes superior, to modern quantum-chemical methods---at negligible computational cost

Heart Diseases Diagnosis Using Artificial Neural Networks

Information technology has virtually altered every aspect of human life in the present era. The application of informatics in the health sector is rapidly gaining prominence and the benefits of this innovative paradigm are being realized across the globe. This evolution produced large number of patients’ data that can be employed by computer technologies and machine learning techniques, and turned into useful information and knowledge. This data can be used to develop expert systems to help in diagnosing some life-threating diseases such as heart diseases, with less cost, processing time and improved diagnosis accuracy. Even though, modern medicine is generating huge amount of data every day, little has been done to use this available data to solve challenges faced in the successful diagnosis of heart diseases. Highlighting the need for more research into the usage of robust data mining techniques to help health care professionals in the diagnosis of heart diseases and other debilitating disease conditions. Based on the foregoing, this thesis aims to develop a health informatics system for the classification of heart diseases using data mining techniques focusing on Radial Basis functions and emerging Neural Networks approach. The presented research involves three development stages; firstly, the development of a preliminary classification system for Coronary Artery Disease (CAD) using Radial Basis Function (RBF) neural networks. The research then deploys the deep learning approach to detect three different types of heart diseases i.e. Sleep Apnea, Arrhythmias and CAD by designing two novel classification systems; the first adopt a novel deep neural network method (with Rectified Linear unit activation) design as the second approach in this thesis and the other implements a novel multilayer kernel machine to mimic the behaviour of deep learning as the third approach. Additionally, this thesis uses a dataset obtained from patients, and employs normalization and feature extraction means to explore it in a unique way that facilitates its usage for training and validating different classification methods. This unique dataset is useful to researchers and practitioners working in heart disease treatment and diagnosis. The findings from the study reveal that the proposed models have high classification performance that is comparable, or perhaps exceed in some cases, the existing automated and manual methods of heart disease diagnosis. Besides, the proposed deep-learning models provide better performance when applied on large data sets (e.g., in the case of Sleep Apnea), with reasonable performance with smaller data sets. The proposed system for clinical diagnoses of heart diseases, contributes to the accurate detection of such disease, and could serve as an important tool in the area of clinic support system. The outcome of this study in form of implementation tool can be used by cardiologists to help them make more consistent diagnosis of heart diseases