Implementing Bayesian Inference with Neural Networks

Embodied agents, be they animals or robots, acquire information about the world through their senses. Embodied agents, however, do not simply lose this information once it passes by, but rather process and store it for future use. The most general theory of how an agent can combine stored knowledge with new observations is Bayesian inference. In this dissertation I present a theory of how embodied agents can learn to implement Bayesian inference with neural networks. By neural network I mean both artificial and biological neural networks, and in my dissertation I address both kinds. On one hand, I develop theory for implementing Bayesian inference in deep generative models, and I show how to train multilayer perceptrons to compute approximate predictions for Bayesian filtering. On the other hand, I show that several models in computational neuroscience are special cases of the general theory that I develop in this dissertation, and I use this theory to model and explain several phenomena in neuroscience. The key contributions of this dissertation can be summarized as follows: - I develop a class of graphical model called nth-order harmoniums. An nth-order harmonium is an n-tuple of random variables, where the conditional distribution of each variable given all the others is always an element of the same exponential family. I show that harmoniums have a recursive structure which allows them to be analyzed at coarser and finer levels of detail. - I define a class of harmoniums called rectified harmoniums, which are constrained to have priors which are conjugate to their posteriors. As a consequence of this, rectified harmoniums afford efficient sampling and learning. - I develop deep harmoniums, which are harmoniums which can be represented by hierarchical, undirected graphs. I develop the theory of rectification for deep harmoniums, and develop a novel algorithm for training deep generative models. - I show how to implement a variety of optimal and near-optimal Bayes filters by combining the solution to Bayes' rule provided by rectified harmoniums, with predictions computed by a recurrent neural network. I then show how to train a neural network to implement Bayesian filtering when the transition and emission distributions are unknown. - I show how some well-established models of neural activity are special cases of the theory I present in this dissertation, and how these models can be generalized with the theory of rectification. - I show how the theory that I present can model several neural phenomena including proprioception and gain-field modulation of tuning curves. - I introduce a library for the programming language Haskell, within which I have implemented all the simulations presented in this dissertation. This library uses concepts from Riemannian geometry to provide a rigorous and efficient environment for implementing complex numerical simulations. I also use the results presented in this dissertation to argue for the fundamental role of neural computation in embodied cognition. I argue, in other words, that before we will be able to build truly intelligent robots, we will need to truly understand biological brains

Signal and data processing for machine olfaction and chemical sensing: A review

Signal and data processing are essential elements in electronic noses as well as in most chemical sensing instruments. The multivariate responses obtained by chemical sensor arrays require signal and data processing to carry out the fundamental tasks of odor identification (classification), concentration estimation (regression), and grouping of similar odors (clustering). In the last decade, important advances have shown that proper processing can improve the robustness of the instruments against diverse perturbations, namely, environmental variables, background changes, drift, etc. This article reviews the advances made in recent years in signal and data processing for machine olfaction and chemical sensing

Deep learning features encode interpretable morphologies within histological images.

Convolutional neural networks (CNNs) are revolutionizing digital pathology by enabling machine learning-based classification of a variety of phenotypes from hematoxylin and eosin (H&E) whole slide images (WSIs), but the interpretation of CNNs remains difficult. Most studies have considered interpretability in a post hoc fashion, e.g. by presenting example regions with strongly predicted class labels. However, such an approach does not explain the biological features that contribute to correct predictions. To address this problem, here we investigate the interpretability of H&E-derived CNN features (the feature weights in the final layer of a transfer-learning-based architecture). While many studies have incorporated CNN features into predictive models, there has been little empirical study of their properties. We show such features can be construed as abstract morphological genes ( mones ) with strong independent associations to biological phenotypes. Many mones are specific to individual cancer types, while others are found in multiple cancers especially from related tissue types. We also observe that mone-mone correlations are strong and robustly preserved across related cancers. Importantly, linear mone-based classifiers can very accurately separate 38 distinct classes (19 tumor types and their adjacent normals, AUC = [Formula: see text] for each class prediction), and linear classifiers are also highly effective for universal tumor detection (AUC = [Formula: see text]). This linearity provides evidence that individual mones or correlated mone clusters may be associated with interpretable histopathological features or other patient characteristics. In particular, the statistical similarity of mones to gene expression values allows integrative mone analysis via expression-based bioinformatics approaches. We observe strong correlations between individual mones and individual gene expression values, notably mones associated with collagen gene expression in ovarian cancer. Mone-expression comparisons also indicate that immunoglobulin expression can be identified using mones in colon adenocarcinoma and that immune activity can be identified across multiple cancer types, and we verify these findings by expert histopathological review. Our work demonstrates that mones provide a morphological H&E decomposition that can be effectively associated with diverse phenotypes, analogous to the interpretability of transcription via gene expression values. Our work also demonstrates mones can be interpreted without using a classifier as a proxy

Nature of the learning algorithms for feedforward neural networks

The neural network model (NN) comprised of relatively simple computing elements, operating in parallel, offers an attractive and versatile framework for exploring a variety of learning structures and processes for intelligent systems. Due to the amount of research developed in the area many types of networks have been defined. The one of interest here is the multi-layer perceptron as it is one of the simplest and it is considered a powerful representation tool whose complete potential has not been adequately exploited and whose limitations need yet to be specified in a formal and coherent framework. This dissertation addresses the theory of generalisation performance and architecture selection for the multi-layer perceptron; a subsidiary aim is to compare and integrate this model with existing data analysis techniques and exploit its potential by combining it with certain constructs from computational geometry creating a reliable, coherent network design process which conforms to the characteristics of a generative learning algorithm, ie. one including mechanisms for manipulating the connections and/or units that comprise the architecture in addition to the procedure for updating the weights of the connections. This means that it is unnecessary to provide an initial network as input to the complete training process.After discussing in general terms the motivation for this study, the multi-layer perceptron model is introduced and reviewed, along with the relevant supervised training algorithm, ie. backpropagation. More particularly, it is argued that a network developed employing this model can in general be trained and designed in a much better way by extracting more information about the domains of interest through the application of certain geometric constructs in a preprocessing stage, specifically by generating the Voronoi Diagram and Delaunav Triangulation [Okabe et al. 92] of the set of points comprising the training set and once a final architecture which performs appropriately on it has been obtained, Principal Component Analysis [Jolliffe 86] is applied to the outputs produced by the units in the network's hidden layer to eliminate the redundant dimensions of this space

Kernel combination via debiased object correspondence analysis

This paper addresses the problem of combining multi-modal kernels in situations in which object correspondence information is unavailable between modalities, for instance, where missing feature values exist, or when using proprietary databases in multi-modal biometrics. The method thus seeks to recover inter-modality kernel information so as to enable classifiers to be built within a composite embedding space. This is achieved through a principled group-wise identification of objects within differing modal kernel matrices in order to form a composite kernel matrix that retains the full freedom of linear kernel combination existing in multiple kernel learning. The underlying principle is derived from the notion of tomographic reconstruction, which has been applied successfully in conventional pattern recognition. In setting out this method, we aim to improve upon object-correspondence insensitive methods, such as kernel matrix combination via the Cartesian product of object sets to which the method defaults in the case of no discovered pairwise object identifications. We benchmark the method against the augmented kernel method, an order-insensitive approach derived from the direct sum of constituent kernel matrices, and also against straightforward additive kernel combination where the correspondence information is given a priori. We find that the proposed method gives rise to substantial performance improvements

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

Kernel combination via debiased object correspondence analysis

This paper addresses the problem of combining multi-modal kernels in situations in which object correspondence information is unavailable between modalities, for instance, where missing feature values exist, or when using proprietary databases in multi-modal biometrics. The method thus seeks to recover inter-modality kernel information so as to enable classifiers to be built within a composite embedding space. This is achieved through a principled group-wise identification of objects within differing modal kernel matrices in order to form a composite kernel matrix that retains the full freedom of linear kernel combination existing in multiple kernel learning. The underlying principle is derived from the notion of tomographic reconstruction, which has been applied successfully in conventional pattern recognition. In setting out this method, we aim to improve upon object-correspondence insensitive methods, such as kernel matrix combination via the Cartesian product of object sets to which the method defaults in the case of no discovered pairwise object identifications. We benchmark the method against the augmented kernel method, an order-insensitive approach derived from the direct sum of constituent kernel matrices, and also against straightforward additive kernel combination where the correspondence information is given a priori. We find that the proposed method gives rise to substantial performance improvements

Recognition of handwritten Arabic characters

The subject of handwritten character recognition has been receiving considerable attention in recent years due to the increased dependence on computers. Several methods for recognizing Latin, Chinese as well as Kanji characters have been proposed. However, work on recognition of Arabic characters has been relatively sparse. Techniques developed for recognizing characters in other languages can not be used for Arabic since the nature of Arabic characters is different. The shape of a character is a function of its location within a word where each character can have two to four different forms. Most of the techniques proposed to date for recognizing Arabic characters have relied on structural and topographic approaches. This thesis introduces a decision-theoretic approach to solve the problem. The proposed method involves, as a first step, digitization of the segmented character. The secondary part of the character (dots and zigzags) are then isolated and identified separately thereby reducing the recognition issue to a 20 class problem or less for each of the character forms. The moments of the horizontal and vertical projections of the remaining primary characters are calculated and normalized with respect to the zero order moment. Simple measures of shape are obtained from the normalized moments and incorporated into a feature vector. Classification is accomplished using quadratic discriminant functions. The approach was evaluated using isolated, handwritten characters from a data base established for this purpose. The classification rates varied from 97.5% to 100% depending on the form of the characters. These results indicate that the technique offers significantly better classification rates in comparison with existing methods

Machine Learning Advances for Practical Problems in Computer Vision

Convolutional neural networks (CNN) have become the de facto standard for computer vision tasks, due to their unparalleled performance and versatility. Although deep learning removes the need for extensive hand engineered features for every task, real world applications of CNNs still often require considerable engineering effort to produce usable results. In this thesis, we explore solutions to problems that arise in practical applications of CNNs. We address a rarely acknowledged weakness of CNN object detectors: the tendency to emit many excess detection boxes per object, which must be pruned by non maximum suppression (NMS). This practice relies on the assumption that highly overlapping boxes are excess, which is problematic when objects are occluding overlapping detections are actually required. Therefore we propose a novel loss function that incentivises a CNN to emit exactly one detection per object, making NMS unnecessary. Another common problem when deploying a CNN in the real world is domain shift - CNNs can be surprisingly vulnerable to sometimes quite subtle differences between the images they encounter at deployment and those they are trained on. We investigate the role that texture plays in domain shift, and propose a novel data augmentation technique using style transfer to train CNNs that are more robust against shifts in texture. We demonstrate that this technique results in better domain transfer on several datasets, without requiring any domain specific knowledge. In collaboration with AstraZeneca, we develop an embedding space for cellular images collected in a high throughput imaging screen as part of a drug discovery project. This uses a combination of techniques to embed the images in 2D space such that similar images are nearby, for the purpose of visualization and data exploration. The images are also clustered automatically, splitting the large dataset into a smaller number of clusters that display a common phenotype. This allows biologists to quickly triage the high throughput screen, selecting a small subset of promising phenotypes for further investigation. Finally, we investigate an unusual form of domain bias that manifested in a real-world visual binary classification project for counterfeit detection. We confirm that CNNs are able to ``cheat'' the task by exploiting a strong correlation between class label and the specific camera that acquired the image, and show that this reliably occurs when the correlation is present. We also investigate the question of how exactly the CNN is able to infer camera type from image pixels, given that this is impossible to the human eye. The contributions in this thesis are of practical value to deep learning practitioners working on a variety of problems in the field of computer vision

Phylogenetic Machine Learning Methods and Application to Mammal Dental Traits and Bioclimatic Variables

Standard machine learning procedures are based on assumption that training and testing data is sampled independently from identical distributions. Comparative data of traits in biological species breaks this assumption. Data instances are related by ancestry relationships, that is phylogeny. In this study, new machine learning procedures are presented that take into account phylogenetic information when fitting predictive models. Phylogenetic statistics for classification accuracy and error are proposed based on the concept of effective sample size. Versions of perceptron training and KNN classification are built on these metrics. Procedures for regularised PGLS regression, phylogenetic KNN regression, neural network regression and regression trees are presented. Properties of phylogenetic perceptron training and KNN regression are studied with synthetic data. Experiments demonstrate that phylogenetic perceptron training improves robustness when the phylogeny is unbalanced. Regularised PGLS and KNN regression are applied to mammal dental traits and environments to both test the algorithms and gain insights in the relationship of mammal teeth and the environment