Browsing by Subject "Probability distributions"

Now showing 1 - 20 of 34

Open Access
Automatic detection of geospatial objects using multiple hierarchical segmentations
(Institute of Electrical and Electronics Engineers, 2008-07) Akçay, H. G.; Aksoy, S.
The object-based analysis of remotely sensed imagery provides valuable spatial and structural information that is complementary to pixel-based spectral information in classification. In this paper, we present novel methods for automatic object detection in high-resolution images by combining spectral information with structural information exploited by using image segmentation. The proposed segmentation algorithm uses morphological operations applied to individual spectral bands using structuring elements in increasing sizes. These operations produce a set of connected components forming a hierarchy of segments for each band. A generic algorithm is designed to select meaningful segments that maximize a measure consisting of spectral homogeneity and neighborhood connectivity. Given the observation that different structures appear more clearly at different scales in different spectral bands, we describe a new algorithm for unsupervised grouping of candidate segments belonging to multiple hierarchical segmentations to find coherent sets of segments that correspond to actual objects. The segments are modeled by using their spectral and textural content, and the grouping problem is solved by using the probabilistic latent semantic analysis algorithm that builds object models by learning the object-conditional probability distributions. The automatic labeling of a segment is done by computing the similarity of its feature distribution to the distribution of the learned object models using the Kullback-Leibler divergence. The performances of the unsupervised segmentation and object detection algorithms are evaluated qualitatively and quantitatively using three different data sets with comparative experiments, and the results show that the proposed methods are able to automatically detect, group, and label segments belonging to the same object classes. © 2008 IEEE.
Open Access
Conditional steady-state bounds for a subset of states in Markov chains
(ACM, 2006-10) Dayar, Tuğrul; Pekergin, N.; Younès, S.
The problem of computing bounds on the conditional steady-state probability vector of a subset of states in finite, ergodic discrete-time Markov chains (DTMCs) is considered. An improved algorithm utilizing the strong stochastic (st-)order is given. On standard benchmarks from the literature and other examples, it is shown that the proposed algorithm performs better than the existing one in the strong stochastic sense. Furthermore, in certain cases the conditional steady-state probability vector of the subset under consideration can be obtained exactly. Copyright 2006 ACM.
Open Access
Continuous and discrete fractional fourier domain decomposition
(IEEE, 2000) Yetik, İ. Şamil; Kutay, M. A.; Özaktaş, H.; Özaktaş, Haldun M.
We introduce the fractional Fourier domain decomposition for continuous and discrete signals and systems. A procedure called pruning, analogous to truncation of the singular-value decomposition, underlies a number of potential applications, among which we discuss fast implementation of space-variant linear systems.
Open Access
Differential privacy with bounded priors: Reconciling utility and privacy in genome-wide association studies
(ACM, 2015-10) Tramèr, F.; Huang, Z.; Hubaux J.-P.; Ayday, Erman
Differential privacy (DP) has become widely accepted as a rigorous definition of data privacy, with stronger privacy guarantees than traditional statistical methods. However, recent studies have shown that for reasonable privacy budgets, differential privacy significantly affects the expected utility. Many alternative privacy notions which aim at relaxing DP have since been proposed, with the hope of providing a better tradeoff between privacy and utility. At CCS'13, Li et al. introduced the membership privacy framework, wherein they aim at protecting against set membership disclosure by adversaries whose prior knowledge is captured by a family of probability distributions. In the context of this framework, we investigate a relaxation of DP, by considering prior distributions that capture more reasonable amounts of background knowledge. We show that for different privacy budgets, DP can be used to achieve membership privacy for various adversarial settings, thus leading to an interesting tradeoff between privacy guarantees and utility. We re-evaluate methods for releasing differentially private χ2-statistics in genome-wide association studies and show that we can achieve a higher utility than in previous works, while still guaranteeing membership privacy in a relevant adversarial setting. © 2015 ACM.
Open Access
An efficient algorithm to extract components of a composite signal
(IEEE, 2000) Özdemir, A. Kemal; Arıkan, Orhan
An efficient algorithm is proposed to extract components of a composite signal. The proposed approach has two stages of processing in which the time-frequency supports of the individual signal components are identified and then the individual components are estimated by performing a simple time-frequency domain incision on the identified support of the component. The use of a recently proposed time-frequency representation [1] significantly improves the performance of the proposed approach by providing very accurate description on the auto-Wigner terms of the composite signal. Then, simple fractional Fourier domain incision provides reliable estimates for each of the signal components in O(N log N) complexity for a composite signal of duration N.
Open Access
Estimating distributions varying in time in a universal manner
(IEEE, 2017) Gökçesu, Kaan; Manış, Eren; Kurt, Ali Emirhan; Yar, Ersin
We investigate the estimation of distributions with time-varying parameters. We introduce an algorithm that achieves the optimal negative likelihood performance against the true probability distribution. We achieve this optimum regret performance without any knowledge about the total change of the parameters of true distribution. Our results are guaranteed to hold in an individual sequence manner such that we have no assumptions on the underlying sequences. Apart from the regret bounds, through synthetic and real life experiments, we demonstrate substantial performance gains with respect to the state-of-the-art probability density estimation algorithms in the literature.
Open Access
Fast computation of the ambiguity function and the Wigner distribution on arbitrary line segments
(IEEE, 2001) Özdemir, A. K.; Arıkan, Orhan
By using the fractional Fourier transformation of the time-domain signals, closed-form expressions for the projections of their auto or cross ambiguity functions are derived. Based on a similar formulation for the projections of the auto and cross Wigner distributions and the well known two-dimensional (2-D) Fourier transformation relationship between the ambiguity and Wigner domains, closed-form expressions are obtained for the slices of both the Wigner distribution and the ambiguity function. By using discretization of the obtained analytical expressions, efficient algorithms are proposed to compute uniformly spaced samples of the Wigner distribution and the ambiguity function located on arbitrary line segments. With repeated use of the proposed algorithms, samples in the Wigner or ambiguity domains can be computed on non-Cartesian sampling grids, such as polar grids.
Open Access
Finding compound structures in images using image segmentation and graph-based knowledge discovery
(IEEE, 2009-07) Zamalieva, Daniya; Aksoy, Selim; Tilton J. C.
We present an unsupervised method for discovering compound image structures that are comprised of simpler primitive objects. An initial segmentation step produces image regions with homogeneous spectral content. Then, the segmentation is translated into a relational graph structure whose nodes correspond to the regions and the edges represent the relationships between these regions. We assume that the region objects that appear together frequently can be considered as strongly related. This relation is modeled using the transition frequencies between neighboring regions, and the significant relations are found as the modes of a probability distribution estimated using the features of these transitions. Experiments using an Ikonos image show that subgraphs found within the graph representing the whole image correspond to parts of different high-level compound structures. ©2009 IEEE.
Open Access
Fitting matrix geometric distributions by model reduction
(Taylor and Francis Inc., 2015) Akar, N.
A novel algorithmic method is proposed to fit matrix geometric distributions of desired order to empirical data or arbitrary discrete distributions. The proposed method effectively combines two existing approaches from two different disciplines: well-established model reduction methods used in system theory and moment matching methods of applied probability that employ second-order discrete phase-type distributions. The proposed approach is validated with exhaustive numerical examples including well-known statistical data. Copyright
Open Access
A general theory on spectral properties of state-homogeneous finite-state quasi-birth-death processes
(Elsevier, 2001) Fadıloğlu, M. M.; Yeralan, S.
In this paper a spectral theory pertaining to Quasi-Birth–Death Processes (QBDs) is presented. The QBD, which is a generalization of the birth–death process, is a powerful tool that can be utilized in modeling many stochastic phenomena. Our theory is based on the application of a matrix polynomial method to obtain the steady-state probabilities in state-homogeneous finite-state QBDs. The method is based on finding the eigenvalue–eigenvector pairs that solve a matrix polynomial equation. Since the computational effort in the solution procedure is independent of the cardinality of the counting set, it has an immediate advantage over other solution procedures. We present and prove different properties relating the quantities that arise in the solution procedure. By also compiling and formalizing the previously known properties, we present a formal unified theory on the spectral properties of QBDs, which furnishes a formal framework to embody much of the previous work. This framework carries the prospect of furthering our understanding of the behavior the modeled systems manifest.
Open Access
GenoGuard: protecting genomic data against brute-force attacks
(IEEE, 2015-05) Huang, Z.; Ayday, Erman; Fellay, Jacques; Hubaux, J-P.; Juels, A.
Secure storage of genomic data is of great and increasing importance. The scientific community's improving ability to interpret individuals' genetic materials and the growing size of genetic database populations have been aggravating the potential consequences of data breaches. The prevalent use of passwords to generate encryption keys thus poses an especially serious problem when applied to genetic data. Weak passwords can jeopardize genetic data in the short term, but given the multi-decade lifespan of genetic data, even the use of strong passwords with conventional encryption can lead to compromise. We present a tool, called Geno Guard, for providing strong protection for genomic data both today and in the long term. Geno Guard incorporates a new theoretical framework for encryption called honey encryption (HE): it can provide information-theoretic confidentiality guarantees for encrypted data. Previously proposed HE schemes, however, can be applied to messages from, unfortunately, a very restricted set of probability distributions. Therefore, Geno Guard addresses the open problem of applying HE techniques to the highly non-uniform probability distributions that characterize sequences of genetic data. In Geno Guard, a potential adversary can attempt exhaustively to guess keys or passwords and decrypt via a brute-force attack. We prove that decryption under any key will yield a plausible genome sequence, and that Geno Guard offers an information-theoretic security guarantee against message-recovery attacks. We also explore attacks that use side information. Finally, we present an efficient and parallelized software implementation of Geno Guard. © 2015 IEEE.
Open Access
Guessing with lies
(IEEE, 2002-06-07) Arıkan, Erdal; Boztaş, S.
A practical algorithm was obtained for directly generating an optimal guessing sequence for guessing under lies. An optimal guessing strategy was defined as one which minimizes the number of average number of guesses in determining the correct value of a random variable. The information-theoretic bounds on the average number of guesses for optimal strategies were also derived.
Open Access
High resolution time frequency representation with significantly reduced cross-terms
(IEEE, 2000-06) Özdemir, A. Kemal; Arıkan, Orhan
A novel algorithm is proposed for efficiently smoothing the slices of the Wigner distribution by exploiting the recently developed relation between the Radon transform of the ambiguity function and the fractional Fourier transformation. The main advantage of the new algorithm is its ability to suppress cross-term interference on chirp-like auto-components without any detrimental effect to the auto-components. For a signal with N samples, the computational complexity of the algorithm is O(N log N) flops for each smoothed slice of the Wigner distribution.
Open Access
İstatistiksel örüntü tanıma teknikleri kullanarak kızılberisi algılayıcılarla hedef ayırdetme
(IEEE, 2006-04) Aytaç, Tayfun; Yüzbaşıoǧlu, Çağrı; Barshan, Billur
This study compares the performances of different statistical pattern recognition techniques to differentiation of commonly encountered features or targets in indoor environments, such as planes, corners, edges, and cylinders, using low-cost infrared sensors. The pattern recognition techniques compared include parametric density estimation, mixture of Gaussians, kernel estimator, k-nearest neighbor classifier, neural network classifier, and support vector machine classifier. A correct differentiation rate of 100% is achieved for six surfaces using parametric differentiation. For three geometries covered with seven different surfaces, best correct differentiation rate (100%) is achieved with mixture of Gaussians classifier with three components. The results demonstrate that simple infrared sensors, when coupled with appropriate processing, can be used to extract substantially more information than such devices are commonly employed. © 2006 IEEE.
Open Access
Language evolution and information theory
(IEEE, 2004-06-07) Ahlswede, R.; Arıkan, Erdal; Bäumer, L.; Deppe, C.
The use of Nowak's model to study the language evolution and to settle a conjecture by Nowak was discussed. These models explained the ways by which natural selection can lead to the gradual emergence of human language. It was shown that the Nowak's conjecture is true for a class of spaces defined by a certain condition on the distance function. A connection between Nowak's model and standard information-theoretic models was indicated.
Open Access
Large deviations of probability rank
(IEEE, 2000) Arıkan, Erdal
Consider a pair of random variables (X,Y) with distribution P. The probability rank function is defined so that G(x|y) = 1 for the most probable outcome x conditional on Y = y, G(x|y) = 2 for the second most probable outcome, and so on, resolving ties between elements with equal probabilities arbitrarily. The function G was considered in [1] in the context of finding the unknown outcome of a random experience by asking question of the form 'Is the outcome equal to x?' sequentially until the actual outcome is determined. The primary focus in [1], and the subsequent works [2], [3], was to find tight bounds on the moments E[G(X|Y)θ]. The present work is closely related to these works but focuses more directly on the large deviations properties of the probability rank function.
Open Access
A matrix analytical method for the discrete time Lindley equation using the generalized Schur decomposition
(ACM, 2006) Akar, Nail
In this paper, we study the discrete time Lindley equation governing an infinite size GI/GI/1 queue. In this queuing system, the arrivals and services are independent and identically distributed but they obey a discrete time matrix geometric distribution not necessarily with finite support. Our GI/GI/1 model allows geometric batch arrivals and also treats late, early, and hybrid arrival models in a unified manner. We reduce the problem of finding the steady state probabilities for the Lindley equation to finding the generalized ordered Schur form of a matrix pair (E, A) where the size of these matrices are the sum, not the product, of the orders of individual arrival and service distributions. The approach taken in this paper is purely matrix analytical and we obtain a matrix geometric representation for the related quantities (queue lengths or waiting times) for the discrete time GI/GI/1 queue using this approach.
Open Access
A new approach to time-frequency localized signal design
(IEEE, 2002) Özdemir, Ahmet Kemal; Aydın, Zafer; Arıkan, Orhan
A novel approach is presented for the design of signals in Wigner Domain. In this method, the desired signal features in the time-frequency domain are specified in two stages. First the user specifies the spine curve around which the energy of the desired signal is distributed in the time-frequency plane. Then, the user specifies the spread of the desired signal energy around the spine. In addition to this fundamentally new way of defining the time-frequency features of the desired signal, the actual synthesis of the signal is performed in a warped fractional Fourier transform approach [1]. After obtaining the designed signal, it is transformed back to the original time domain providing the final result of the new signal synthesis technique. In contrast to the conventional algorithms, the proposed method provides very good results even if the inner cross-term structure of the desired signal is not specified.
Open Access
Noise-enhanced M-ary hypothesis-testing in the minimax framework
(IEEE, 2009-09) Bayram, Suat; Gezici, Sinan
In this study, the effects of adding independent noise to observations of a suboptimal detector are studied for M-ary hypothesis-testing problems according to the minimax criterion. It is shown that the optimal additional noise can be represented by a randomization of at most M signal values under certain conditions. In addition, a convex relaxation approach is proposed to obtain an accurate approximation to the noise probability distribution in polynomial time. Furthermore, sufficient conditions are presented to determine when additional noise can or cannot improve the performance of a given detector. Finally, a numerical example is presented. © 2009 IEEE.
Open Access
Non-Boltzmann stationary distributions and nonequilibrium relations in active baths
(American Physical Society, 2016-12) Argun, A.; Moradi A.-R.; Pinçe, E.; Bagci, G. B.; Imparato, A.; Volpe, G.
Most natural and engineered processes, such as biomolecular reactions, protein folding, and population dynamics, occur far from equilibrium and therefore cannot be treated within the framework of classical equilibrium thermodynamics. Here we experimentally study how some fundamental thermodynamic quantities and relations are affected by the presence of the nonequilibrium fluctuations associated with an active bath. We show in particular that, as the confinement of the particle increases, the stationary probability distribution of a Brownian particle confined within a harmonic potential becomes non-Boltzmann, featuring a transition from a Gaussian distribution to a heavy-tailed distribution. Because of this, nonequilibrium relations (e.g., the Jarzynski equality and Crooks fluctuation theorem) cannot be applied. We show that these relations can be restored by using the effective potential associated with the stationary probability distribution. We corroborate our experimental findings with theoretical arguments.