29,120 research outputs found
The Topology of Negatively Associated Distributions
We consider the sets of negatively associated (NA) and negatively correlated
(NC) distributions as subsets of the space of all probability
distributions on , in terms of their relative topological
structures within the topological space of all measures on a given measurable
space. We prove that the class of NA distributions has a non-empty interior
with respect to the topology of the total variation metric on . We
show however that this is not the case in the weak topology (i.e. the topology
of convergence in distribution), unless the underlying probability space is
finite. We consider both the convexity and the connectedness of these classes
of probability measures, and also consider the two classes on their (widely
studied) restrictions to the Boolean cube in
An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal
Nonsinusoidal oscillatory signals are everywhere. In practice, the
nonsinusoidal oscillatory pattern, modeled as a 1-periodic wave-shape function
(WSF), might vary from cycle to cycle. When there are finite different WSFs,
, so that the WSF jumps from one to another suddenly, the
different WSFs and jumps encode useful information. We present an iterative
warping and clustering algorithm to estimate from a
nonstationary oscillatory signal with time-varying amplitude and frequency, and
hence the change points of the WSFs. The algorithm is a novel combination of
time-frequency analysis, singular value decomposition entropy and vector
spectral clustering. We demonstrate the efficiency of the proposed algorithm
with simulated and real signals, including the voice signal, arterial blood
pressure, electrocardiogram and accelerometer signal. Moreover, we provide a
mathematical justification of the algorithm under the assumption that the
amplitude and frequency of the signal are slowly time-varying and there are
finite change points that model sudden changes from one wave-shape function to
another one.Comment: 39 pages, 11 figure
Audio-Visual Automatic Speech Recognition Towards Education for Disabilities
Education is a fundamental right that enriches everyone’s life. However, physically challenged people often debar from the general and advanced education system. Audio-Visual Automatic Speech Recognition (AV-ASR) based system is useful to improve the education of physically challenged people by providing hands-free computing. They can communicate to the learning system through AV-ASR. However, it is challenging to trace the lip correctly for visual modality. Thus, this paper addresses the appearance-based visual feature along with the co-occurrence statistical measure for visual speech recognition. Local Binary Pattern-Three Orthogonal Planes (LBP-TOP) and Grey-Level Co-occurrence Matrix (GLCM) is proposed for visual speech information. The experimental results show that the proposed system achieves 76.60 % accuracy for visual speech and 96.00 % accuracy for audio speech recognition
Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio
This paper reviews the most common situations where one or more regularity
conditions which underlie classical likelihood-based parametric inference fail.
We identify three main classes of problems: boundary problems, indeterminate
parameter problems -- which include non-identifiable parameters and singular
information matrices -- and change-point problems. The review focuses on the
large-sample properties of the likelihood ratio statistic. We emphasize
analytical solutions and acknowledge software implementations where available.
We furthermore give summary insight about the possible tools to derivate the
key results. Other approaches to hypothesis testing and connections to
estimation are listed in the annotated bibliography of the Supplementary
Material
Offline and Online Models for Learning Pairwise Relations in Data
Pairwise relations between data points are essential for numerous machine learning algorithms. Many representation learning methods consider pairwise relations to identify the latent features and patterns in the data. This thesis, investigates learning of pairwise relations from two different perspectives: offline learning and online learning.The first part of the thesis focuses on offline learning by starting with an investigation of the performance modeling of a synchronization method in concurrent programming using a Markov chain whose state transition matrix models pairwise relations between involved cores in a computer process.Then the thesis focuses on a particular pairwise distance measure, the minimax distance, and explores memory-efficient approaches to computing this distance by proposing a hierarchical representation of the data with a linear memory requirement with respect to the number of data points, from which the exact pairwise minimax distances can be derived in a memory-efficient manner. Then, a memory-efficient sampling method is proposed that follows the aforementioned hierarchical representation of the data and samples the data points in a way that the minimax distances between all data points are maximally preserved. Finally, the thesis proposes a practical non-parametric clustering of vehicle motion trajectories to annotate traffic scenarios based on transitive relations between trajectories in an embedded space.The second part of the thesis takes an online learning perspective, and starts by presenting an online learning method for identifying bottlenecks in a road network by extracting the minimax path, where bottlenecks are considered as road segments with the highest cost, e.g., in the sense of travel time. Inspired by real-world road networks, the thesis assumes a stochastic traffic environment in which the road-specific probability distribution of travel time is unknown. Therefore, it needs to learn the parameters of the probability distribution through observations by modeling the bottleneck identification task as a combinatorial semi-bandit problem. The proposed approach takes into account the prior knowledge and follows a Bayesian approach to update the parameters. Moreover, it develops a combinatorial variant of Thompson Sampling and derives an upper bound for the corresponding Bayesian regret. Furthermore, the thesis proposes an approximate algorithm to address the respective computational intractability issue.Finally, the thesis considers contextual information of road network segments by extending the proposed model to a contextual combinatorial semi-bandit framework and investigates and develops various algorithms for this contextual combinatorial setting
On the competitive facility location problem with a Bayesian spatial interaction model
The competitive facility location problem arises when businesses plan to enter a new market or expand their presence. We introduce a Bayesian spatial interaction model which provides probabilistic estimates on location-specific revenues and then formulate a mathematical framework to simultaneously identify the location and design of new facilities that maximise revenue. To solve the allocation optimisation problem, we develop a hierarchical search algorithm and associated sampling techniques that explore geographic regions of varying spatial resolution. We demonstrate the approach by producing optimal facility locations and corresponding designs for two large-scale applications in the supermarket and pub sectors of Greater London
High-Dimensional Private Empirical Risk Minimization by Greedy Coordinate Descent
In this paper, we study differentially private empirical risk minimization
(DP-ERM). It has been shown that the worst-case utility of DP-ERM reduces
polynomially as the dimension increases. This is a major obstacle to privately
learning large machine learning models. In high dimension, it is common for
some model's parameters to carry more information than others. To exploit this,
we propose a differentially private greedy coordinate descent (DP-GCD)
algorithm. At each iteration, DP-GCD privately performs a coordinate-wise
gradient step along the gradients' (approximately) greatest entry. We show
theoretically that DP-GCD can achieve a logarithmic dependence on the dimension
for a wide range of problems by naturally exploiting their structural
properties (such as quasi-sparse solutions). We illustrate this behavior
numerically, both on synthetic and real datasets
Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field model in 3+1 dimensions
Binary black hole simulations become increasingly more computationally
expensive with smaller mass ratios, partly because of the longer evolution
time, and partly because the lengthscale disparity dictates smaller time steps.
The program initiated by Dhesi et al. (arXiv:2109.03531) explores a method for
alleviating the scale disparity in simulations with mass ratios in the
intermediate astrophysical range (), where
purely perturbative methods may not be adequate. A region ("worldtube") much
larger than the small black hole is excised from the numerical domain, and
replaced with an analytical model approximating a tidally deformed black hole.
Here we apply this idea to a toy model of a scalar charge in a fixed circular
geodesic orbit around a Schwarzschild black hole, solving for the massless
Klein-Gordon field. This is a first implementation of the worldtube excision
method in full 3+1 dimensions. We demonstrate the accuracy and efficiency of
the method, and discuss the steps towards applying it for evolving orbits and,
ultimately, in the binary black-hole scenario. Our implementation is publicly
accessible in the SpECTRE numerical relativity code.Comment: 19 pages, 10 figure
Fast approximate Barnes interpolation: illustrated by Python-Numba implementation fast-barnes-py v1.0
Barnes interpolation is a method that is widely used in geospatial sciences like meteorology to remodel data values recorded at irregularly distributed points into a representative analytical field. When implemented naively, the effort to calculate Barnes interpolation depends on the product of the number of sample points N and the number of grid points W×H, resulting in a computational complexity of O(N⋅W⋅H). In the era of highly resolved grids and overwhelming numbers of sample points, which originate, e.g., from the Internet of Things or crowd-sourced data, this computation can be quite demanding, even on high-performance machines.
This paper presents new approaches of how very good approximations of Barnes interpolation can be implemented using fast algorithms that have a computational complexity of O(N+Wâ‹…H). Two use cases in particular are considered, namely (1)Â where the used grid is embedded in the Euclidean plane and (2)Â where the grid is located on the unit sphere.</p
Four Lectures on the Random Field Ising Model, Parisi-Sourlas Supersymmetry, and Dimensional Reduction
Numerical evidence suggests that the Random Field Ising Model loses
Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4
and 5 dimensions, while a related model of branched polymers retains these
features in any . These notes give a leisurely introduction to a recent
theory, developed jointly with A. Kaviraj and E. Trevisani, which aims to
explain these facts. Based on the lectures given in Cortona and at the IHES in
2022.Comment: 55 pages, 11 figures; v2 - minor changes, mentioned forthcoming work
by Fytas et a
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