Reasoning about Independence in Probabilistic Models of Relational Data

We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data inaccurately infers conditional independence. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related wor

Causal Discovery for Relational Domains: Representation, Reasoning, and Learning

Many domains are currently experiencing the growing trend to record and analyze massive, observational data sets with increasing complexity. A commonly made claim is that these data sets hold potential to transform their corresponding domains by providing previously unknown or unexpected explanations and enabling informed decision-making. However, only knowledge of the underlying causal generative process, as opposed to knowledge of associational patterns, can support such tasks. Most methods for traditional causal discovery—the development of algorithms that learn causal structure from observational data—are restricted to representations that require limiting assumptions on the form of the data. Causal discovery has almost exclusively been applied to directed graphical models of propositional data that assume a single type of entity with independence among instances. However, most real-world domains are characterized by systems that involve complex interactions among multiple types of entities. Many state-of-the-art methods in statistics and machine learning that address such complex systems focus on learning associational models, and they are oftentimes mistakenly interpreted as causal. The intersection between causal discovery and machine learning in complex systems is small. The primary objective of this thesis is to extend causal discovery to such complex systems. Specifically, I formalize a relational representation and model that can express the causal and probabilistic dependencies among the attributes of interacting, heterogeneous entities. I show that the traditional method for reasoning about statistical independence from model structure fails to accurately derive conditional independence facts from relational models. I introduce a new theory—relational d-separation—and a novel, lifted representation—the abstract ground graph—that supports a sound, complete, and computationally efficient method for algorithmically deriving conditional independencies from probabilistic models of relational data. The abstract ground graph representation also presents causal implications that enable the detection of causal direction for bivariate relational dependencies without parametric assumptions. I leverage these implications and the theoretical framework of relational d-separation to develop a sound and complete algorithm—the relational causal discovery (RCD) algorithm—that learns causal structure from relational data

Augmented Mitotic Cell Count using Field Of Interest Proposal

Histopathological prognostication of neoplasia including most tumor grading systems are based upon a number of criteria. Probably the most important is the number of mitotic figures which are most commonly determined as the mitotic count (MC), i.e. number of mitotic figures within 10 consecutive high power fields. Often the area with the highest mitotic activity is to be selected for the MC. However, since mitotic activity is not known in advance, an arbitrary choice of this region is considered one important cause for high variability in the prognostication and grading. In this work, we present an algorithmic approach that first calculates a mitotic cell map based upon a deep convolutional network. This map is in a second step used to construct a mitotic activity estimate. Lastly, we select the image segment representing the size of ten high power fields with the overall highest mitotic activity as a region proposal for an expert MC determination. We evaluate the approach using a dataset of 32 completely annotated whole slide images, where 22 were used for training of the network and 10 for test. We find a correlation of r=0.936 in mitotic count estimate.Comment: 6 pages, submitted to BVM 2019 (bvm-workshop.org

Identifying Independence in Relational Models

The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for deriving conditional independence in relational models. We provide a sound, complete, and computationally efficient method for relational d-separation, and we present empirical results that demonstrate effectiveness.Comment: This paper has been revised and expanded. See "Reasoning about Independence in Probabilistic Models of Relational Data" http://arxiv.org/abs/1302.438

Deep Denoising for Hearing Aid Applications

Reduction of unwanted environmental noises is an important feature of today's hearing aids (HA), which is why noise reduction is nowadays included in almost every commercially available device. The majority of these algorithms, however, is restricted to the reduction of stationary noises. In this work, we propose a denoising approach based on a three hidden layer fully connected deep learning network that aims to predict a Wiener filtering gain with an asymmetric input context, enabling real-time applications with high constraints on signal delay. The approach is employing a hearing instrument-grade filter bank and complies with typical hearing aid demands, such as low latency and on-line processing. It can further be well integrated with other algorithms in an existing HA signal processing chain. We can show on a database of real world noise signals that our algorithm is able to outperform a state of the art baseline approach, both using objective metrics and subject tests.Comment: submitted to IWAENC 201

Application of Ewald's Method for Efficient Summation of Dyon Long-Range Potentials

We study a model of dyons for SU(2) Yang-Mills theory at finite temperature T < T_c, in particular its ability to generate a confining force between a static quark antiquark pair. The interaction between dyons corresponds to a long-range 1/r potential, which in naive treatments with a finite number of dyons typically gives rise to severe finite volume effects. To avoid such effects we apply the so-called Ewald method, which has its origin in solid state physics. The basic idea of Ewald's method is to consider a finite number of dyons inside a finite cubic volume and enforce periodicity of this volume. We explain the technicalities of Ewald's method and outline how the method can be applied to a wider class of 1/r^p long-range potentials.Comment: 8 pages, 4 figures, contribution to conference "Confinement X

Symmetric Galerkin boundary element method.

This review concerns a methodology for solving numerically, to engineering purposes, boundary and initial-boundary value roblems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form; the discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager's sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions, some quadratic forms have a clear energy meaning, variational properties characterize the solutions and other results, invalid in traditional boundary element methods, enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, computer implementations. Areas and aspects which at present require further research are dentified and comparative assessments are attempted with respect to traditional boundary integral-element methods