JIDT: An information-theoretic toolkit for studying the dynamics of complex systems

Complex systems are increasingly being viewed as distributed information processing systems, particularly in the domains of computational neuroscience, bioinformatics and Artificial Life. This trend has resulted in a strong uptake in the use of (Shannon) information-theoretic measures to analyse the dynamics of complex systems in these fields. We introduce the Java Information Dynamics Toolkit (JIDT): a Google code project which provides a standalone, (GNU GPL v3 licensed) open-source code implementation for empirical estimation of information-theoretic measures from time-series data. While the toolkit provides classic information-theoretic measures (e.g. entropy, mutual information, conditional mutual information), it ultimately focusses on implementing higher-level measures for information dynamics. That is, JIDT focusses on quantifying information storage, transfer and modification, and the dynamics of these operations in space and time. For this purpose, it includes implementations of the transfer entropy and active information storage, their multivariate extensions and local or pointwise variants. JIDT provides implementations for both discrete and continuous-valued data for each measure, including various types of estimator for continuous data (e.g. Gaussian, box-kernel and Kraskov-Stoegbauer-Grassberger) which can be swapped at run-time due to Java's object-oriented polymorphism. Furthermore, while written in Java, the toolkit can be used directly in MATLAB, GNU Octave, Python and other environments. We present the principles behind the code design, and provide several examples to guide users.Comment: 37 pages, 4 figure

An Adaptive Locally Connected Neuron Model: Focusing Neuron

This paper presents a new artificial neuron model capable of learning its receptive field in the topological domain of inputs. The model provides adaptive and differentiable local connectivity (plasticity) applicable to any domain. It requires no other tool than the backpropagation algorithm to learn its parameters which control the receptive field locations and apertures. This research explores whether this ability makes the neuron focus on informative inputs and yields any advantage over fully connected neurons. The experiments include tests of focusing neuron networks of one or two hidden layers on synthetic and well-known image recognition data sets. The results demonstrated that the focusing neurons can move their receptive fields towards more informative inputs. In the simple two-hidden layer networks, the focusing layers outperformed the dense layers in the classification of the 2D spatial data sets. Moreover, the focusing networks performed better than the dense networks even when 70$\%$ of the weights were pruned. The tests on convolutional networks revealed that using focusing layers instead of dense layers for the classification of convolutional features may work better in some data sets.Comment: 45 pages, a national patent filed, submitted to Turkish Patent Office, No: -2017/17601, Date: 09.11.201

Bits from Biology for Computational Intelligence

Computational intelligence is broadly defined as biologically-inspired computing. Usually, inspiration is drawn from neural systems. This article shows how to analyze neural systems using information theory to obtain constraints that help identify the algorithms run by such systems and the information they represent. Algorithms and representations identified information-theoretically may then guide the design of biologically inspired computing systems (BICS). The material covered includes the necessary introduction to information theory and the estimation of information theoretic quantities from neural data. We then show how to analyze the information encoded in a system about its environment, and also discuss recent methodological developments on the question of how much information each agent carries about the environment either uniquely, or redundantly or synergistically together with others. Last, we introduce the framework of local information dynamics, where information processing is decomposed into component processes of information storage, transfer, and modification -- locally in space and time. We close by discussing example applications of these measures to neural data and other complex systems

Adaptive sequential feature selection in visual perception and pattern recognition

In the human visual system, one of the most prominent functions of the extensive feedback from the higher brain areas within and outside of the visual cortex is attentional modulation. The feedback helps the brain to concentrate its resources on visual features that are relevant for recognition, i. e. it iteratively selects certain aspects of the visual scene for refined processing by the lower areas until the inference process in the higher areas converges to a single hypothesis about this scene. In order to minimize a number of required selection-refinement iterations, one has to find a short sequence of maximally informative portions of the visual input. Since the feedback is not static, the selection process is adapted to a scene that should be recognized. To find a scene-specific subset of informative features, the adaptive selection process on every iteration utilizes results of previous processing in order to reduce the remaining uncertainty about the visual scene. This phenomenon inspired us to develop a computational algorithm solving a visual classification task that would incorporate such principle, adaptive feature selection. It is especially interesting because usually feature selection methods are not adaptive as they define a unique set of informative features for a task and use them for classifying all objects. However, an adaptive algorithm selects features that are the most informative for the particular input. Thus, the selection process should be driven by statistics of the environment concerning the current task and the object to be classified. Applied to a classification task, our adaptive feature selection algorithm favors features that maximally reduce the current class uncertainty, which is iteratively updated with values of the previously selected features that are observed on the testing sample. In information-theoretical terms, the selection criterion is the mutual information of a class variable and a feature-candidate conditioned on the already selected features, which take values observed on the current testing sample. Then, the main question investigated in this thesis is whether the proposed adaptive way of selecting features is advantageous over the conventional feature selection and in which situations. Further, we studied whether the proposed adaptive information-theoretical selection scheme, which is a computationally complex algorithm, is utilized by humans while they perform a visual classification task. For this, we constructed a psychophysical experiment where people had to select image parts that as they think are relevant for classification of these images. We present the analysis of behavioral data where we investigate whether human strategies of task-dependent selective attention can be explained by a simple ranker based on the mutual information, a more complex feature selection algorithm based on the conventional static mutual information and the proposed here adaptive feature selector that mimics a mechanism of the iterative hypothesis refinement. Hereby, the main contribution of this work is the adaptive feature selection criterion based on the conditional mutual information. Also it is shown that such adaptive selection strategy is indeed used by people while performing visual classification.:1. Introduction 2. Conventional feature selection 3. Adaptive feature selection 4. Experimental investigations of ACMIFS 5. Information-theoretical strategies of selective attention 6. Discussion Appendix Bibliograph

Modern optical astronomy: technology and impact of interferometry

The present `state of the art' and the path to future progress in high spatial resolution imaging interferometry is reviewed. The review begins with a treatment of the fundamentals of stellar optical interferometry, the origin, properties, optical effects of turbulence in the Earth's atmosphere, the passive methods that are applied on a single telescope to overcome atmospheric image degradation such as speckle interferometry, and various other techniques. These topics include differential speckle interferometry, speckle spectroscopy and polarimetry, phase diversity, wavefront shearing interferometry, phase-closure methods, dark speckle imaging, as well as the limitations imposed by the detectors on the performance of speckle imaging. A brief account is given of the technological innovation of adaptive-optics (AO) to compensate such atmospheric effects on the image in real time. A major advancement involves the transition from single-aperture to the dilute-aperture interferometry using multiple telescopes. Therefore, the review deals with recent developments involving ground-based, and space-based optical arrays. Emphasis is placed on the problems specific to delay-lines, beam recombination, polarization, dispersion, fringe-tracking, bootstrapping, coherencing and cophasing, and recovery of the visibility functions. The role of AO in enhancing visibilities is also discussed. The applications of interferometry, such as imaging, astrometry, and nulling are described. The mathematical intricacies of the various `post-detection' image-processing techniques are examined critically. The review concludes with a discussion of the astrophysical importance and the perspectives of interferometry.Comment: 65 pages LaTeX file including 23 figures. Reviews of Modern Physics, 2002, to appear in April issu