Ising Graphical Model

The Ising model is an important model in statistical physics, with over 10,000 papers published on the topic. This model assumes binary variables and only local pairwise interactions between neighbouring nodes. Inference for the general Ising model is NP-hard; this includes tasks such as calculating the partition function, finding a lowest-energy (ground) state and computing marginal probabilities. Past approaches have proceeded by working with classes of tractable Ising models, such as Ising models defined on a planar graph. For such models, the partition function and ground state can be computed exactly in polynomial time by establishing a correspondence with perfect matchings in a related graph. In this thesis we continue this line of research. In particular we simplify previous inference algorithms for the planar Ising model. The key to our construction is the complementary correspondence between graph cuts of the model graph and perfect matchings of its expanded dual. We show that our exact algorithms are effective and efficient on a number of real-world machine learning problems. We also investigate heuristic methods for approximating ground states of non-planar Ising models. We show that in this setting our approximative algorithms are superior than current state-of-the-art methods

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Machine learning of image analysis with convolutional networks and topological constraints

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 130-140).We present an approach to solving computer vision problems in which the goal is to produce a high-dimensional, pixel-based interpretation of some aspect of the underlying structure of an image. Such tasks have traditionally been categorized as ''low-level vision'' problems, and examples include image denoising, boundary detection, and motion estimation. Our approach is characterized by two main elements, both of which represent a departure from previous work. The first is a focus on convolutional networks, a machine learning strategy that operates directly on an input image with no use of hand-designed features and employs many thousands of free parameters that are learned from data. Previous work in low-level vision has been largely focused on completely hand-designed algorithms or learning methods with a hand-designed feature space. We demonstrate that a learning approach with high model complexity, but zero prior knowledge about any specific image domain, can outperform existing techniques even in the challenging area of natural image processing. We also present results that establish how convolutional networks are closely related to Markov random fields (MRFs), a popular probabilistic approach to image analysis, but can in practice can achieve significantly greater model complexity. The second aspect of our approach is the use of domain specific cost functions and learning algorithms that reflect the structured nature of certain prediction problems in image analysis.(cont.) In particular, we show how concepts from digital topology can be used in the context of boundary detection to both evaluate and optimize the high-order property of topological accuracy. We demonstrate that these techniques can significantly improve the machine learning approach and outperform state of the art boundary detection and segmentation methods. Throughout our work we maintain a special interest and focus on application of our methods to connectomics, an emerging scientific discipline that seeks high-throughput methods for recovering neural connectivity data from brains. This application requires solving low-level image analysis problems on a tera-voxel or peta-voxel scale, and therefore represents an extremely challenging and exciting arena for the development of computer vision methods.by Viren Jain.Ph.D

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

The Observational Signatures of Cosmic Strings

Cosmic strings were postulated by Kibble in 1976 and, from a theoretical point of view, their existence finds support in modern superstring theories, both in compactification models and in theories with extended additional dimensions. One of the best observational evidences for cosmic strings is the gravitational lensing effects they produce. A first effect is produced by an intervening string along the line of sight which splits in two components (double images) faint background galaxies, thus forming a chain of lensed galaxies along the path of the string. The second optical method is the serendipity discovery through anomalous lensing of extended objects. The huge ratio existing between the string width and length leads to a sort of step function signature on the gravitationally lensed images of background sources. The optical research of cosmic strings signatures suffers from many spurious effects mainly induced by the fact that, in order to be effective, the detection of background galaxies needs to be pushed down to very low flux limits. At these flux levels photometric errors, as well as noise statistics increase the number of spurious detections and, for instance, an application to the Sloan Digital Sky Survey leads to an huge and unrealistic number of candidate pairs. One way to minimize the contamination introduced in the catalogues by the spurious detection, is to increase the contrast by selecting pairs in the 3D space, i.e. by attributing to each galaxy a redshift estimate. At this purpose, a new method for photometric redshifts estimation has been created. The method is based on multiwavelength photometry and on a combination of various data mining techniques developed under the EuroVO and NVO frameworks for data gathering, pre-processing and mining, while relying on the scaling capabilities of the computing grid. This method allowed us to obtain photometric redshifts with an increased accuracy (up to 30%) with respect to the literature. The second fundamental observational evidence for cosmic strings is the signature they are expected to leave in the CMB a signature which may be sought for in the available WMAP data and in the soon to come Planck data. Theory shows that a moving string should produce a step-like discontinuity of low S/N ratio in the CMB, as a consequence of the Doppler shift due to the relative velocity between the string and the observer, thus causing the temperature distribution to deviate from a Gaussian. In the simplifying assumption that the string is a straight discontinuity in space time, we used the S.Co.P.E. computational grid to produce a large number of simulations covering a wide range of values for the velocity of the string, its direction and its distance from the observer. Simulations are produced using a C++ code that generates realistic maps of the CMB temperature distribution in presence of a straight cosmic string. By varying its characteristic parameters, it is possible to explore the signatures left by various types of moving strings. In order to amplify the step-like discontinuity and smooth the noise, maps are then subjected to a “squeezing” procedure. Successively, on the “squeezed” maps, we tested some filters that recognizes high value differences between close pixels. The excellent results of our filter on simulations prompted us to apply it on WMAP 5 years data