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Carlos Guestrin - One of the best experts on this subject based on the ideXlab platform.
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Efficient Probabilistic Inference with Partial Ranking Queries
arXiv: Learning, 2012Co-Authors: Jonathan Huang, Ashish Kapoor, Carlos GuestrinAbstract:Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or Probabilistic Independence about these underlying distributions. We approach the modeling problem from the computational principle that one should make structural assumptions which allow for efficient calculation of typical Probabilistic queries. For ranking models, "typical" queries predominantly take the form of partial ranking queries (e.g., given a user's top-k favorite movies, what are his preferences over remaining movies?). In this paper, we argue that riffled Independence factorizations proposed in recent literature [7, 8] are a natural structural assumption for ranking distributions, allowing for particularly efficient processing of partial ranking queries.
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uncovering the riffled Independence structure of ranked data
Electronic Journal of Statistics, 2012Co-Authors: Jonathan Huang, Carlos GuestrinAbstract:Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit Probabilistic Independence, but as we argue, full Independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of Independence structures, called riffled Independence, encompassing a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled Independence, one draws two permutations independently, then performs the riffle shuffle, common in card games, to combine the two permutations to form a single permutation. Within the context of ranking, riffled Independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. In this paper, we provide a formal introduction to riffled Independence and propose an automated method for discovering sets of items which are riffle independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on riffled Independence. AMS 2000 subject classifications: Primary 68T37, 60C05; secondary 60B15.
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UAI - Efficient Probabilistic inference with partial ranking queries
2011Co-Authors: Jonathan Huang, Ashish Kapoor, Carlos GuestrinAbstract:Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or Probabilistic Independence about these underlying distributions. We approach the modeling problem from the computational principle that one should make structural assumptions which allow for efficient calculation of typical Probabilistic queries. For ranking models, "typical" queries predominantly take the form of partial ranking queries (e.g., given a user's top-k favorite movies, what are his preferences over remaining movies?). In this paper, we argue that riffled Independence factorizations proposed in recent literature [7, 8] are a natural structural assumption for ranking distributions, allowing for particularly efficient processing of partial ranking queries.
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ICML - Learning Hierarchical Riffle Independent Groupings from Rankings
2010Co-Authors: Jonathan Huang, Carlos GuestrinAbstract:Riffled Independence is a generalized notion of Probabilistic Independence that has been shown to be naturally applicable to ranked data. In the riffled Independence model, one assigns rankings to two disjoint sets of items independently, then in a second stage, interleaves (or riffles) the two rankings together to form a full ranking, as if by shuffling a deck of cards. Because of this interleaving stage, it is much more difficult to detect riffled Independence than ordinary Independence. In this paper, we provide the first automated method for discovering sets of items which are riffle independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on riffled Independence.
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NIPS - Riffled Independence for Ranked Data
2009Co-Authors: Jonathan Huang, Carlos GuestrinAbstract:Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit Probabilistic Independence, but as we argue, full Independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of Independence structures, called riffled Independence, which encompasses a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled Independence, one draws two permutations independently, then performs the riffle shuffle, common in card games, to combine the two permutations to form a single permutation. In ranking, riffled Independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. We provide a formal introduction and present algorithms for using riffled Independence within Fourier-theoretic frameworks which have been explored by a number of recent papers.
Jonathan Huang - One of the best experts on this subject based on the ideXlab platform.
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Efficient Probabilistic Inference with Partial Ranking Queries
arXiv: Learning, 2012Co-Authors: Jonathan Huang, Ashish Kapoor, Carlos GuestrinAbstract:Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or Probabilistic Independence about these underlying distributions. We approach the modeling problem from the computational principle that one should make structural assumptions which allow for efficient calculation of typical Probabilistic queries. For ranking models, "typical" queries predominantly take the form of partial ranking queries (e.g., given a user's top-k favorite movies, what are his preferences over remaining movies?). In this paper, we argue that riffled Independence factorizations proposed in recent literature [7, 8] are a natural structural assumption for ranking distributions, allowing for particularly efficient processing of partial ranking queries.
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uncovering the riffled Independence structure of ranked data
Electronic Journal of Statistics, 2012Co-Authors: Jonathan Huang, Carlos GuestrinAbstract:Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit Probabilistic Independence, but as we argue, full Independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of Independence structures, called riffled Independence, encompassing a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled Independence, one draws two permutations independently, then performs the riffle shuffle, common in card games, to combine the two permutations to form a single permutation. Within the context of ranking, riffled Independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. In this paper, we provide a formal introduction to riffled Independence and propose an automated method for discovering sets of items which are riffle independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on riffled Independence. AMS 2000 subject classifications: Primary 68T37, 60C05; secondary 60B15.
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UAI - Efficient Probabilistic inference with partial ranking queries
2011Co-Authors: Jonathan Huang, Ashish Kapoor, Carlos GuestrinAbstract:Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or Probabilistic Independence about these underlying distributions. We approach the modeling problem from the computational principle that one should make structural assumptions which allow for efficient calculation of typical Probabilistic queries. For ranking models, "typical" queries predominantly take the form of partial ranking queries (e.g., given a user's top-k favorite movies, what are his preferences over remaining movies?). In this paper, we argue that riffled Independence factorizations proposed in recent literature [7, 8] are a natural structural assumption for ranking distributions, allowing for particularly efficient processing of partial ranking queries.
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ICML - Learning Hierarchical Riffle Independent Groupings from Rankings
2010Co-Authors: Jonathan Huang, Carlos GuestrinAbstract:Riffled Independence is a generalized notion of Probabilistic Independence that has been shown to be naturally applicable to ranked data. In the riffled Independence model, one assigns rankings to two disjoint sets of items independently, then in a second stage, interleaves (or riffles) the two rankings together to form a full ranking, as if by shuffling a deck of cards. Because of this interleaving stage, it is much more difficult to detect riffled Independence than ordinary Independence. In this paper, we provide the first automated method for discovering sets of items which are riffle independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on riffled Independence.
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NIPS - Riffled Independence for Ranked Data
2009Co-Authors: Jonathan Huang, Carlos GuestrinAbstract:Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit Probabilistic Independence, but as we argue, full Independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of Independence structures, called riffled Independence, which encompasses a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled Independence, one draws two permutations independently, then performs the riffle shuffle, common in card games, to combine the two permutations to form a single permutation. In ranking, riffled Independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. We provide a formal introduction and present algorithms for using riffled Independence within Fourier-theoretic frameworks which have been explored by a number of recent papers.
Juan D. Tardós - One of the best experts on this subject based on the ideXlab platform.
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IROS - Scalable SLAM building conditionally independent local maps
2007 IEEE RSJ International Conference on Intelligent Robots and Systems, 2007Co-Authors: Pedro Pinies, Juan D. TardósAbstract:Local maps algorithms have demonstrated to be well suited for mapping large environments as can reduce the computational cost and improve the consistency of the final estimation. In this paper we present a new technique that allows the use of local mapping algorithms in the context of EKF SLAM but without the constrain of Probabilistic Independence between local maps. By means of this procedure, salient features of the environment or vehicle state components as velocity or global attitude, can be shared between local maps without affecting the posterior joining process or introducing any undesirable approximations in the final global map estimate. The overload cost introduced by the technique is minimum since building up local maps does not require any additional operations apart from the usual EKF steps. As the algorithm works with covariance matrices, well-known data association techniques can be used in the usual manner. To test the technique, experimental results using a monocular camera in an outdoor environment are provided. The initialization of the features is based on the inverse depth algorithm.
Sean D Lawley - One of the best experts on this subject based on the ideXlab platform.
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Anomalous reaction-diffusion equations for linear reactions.
Physical review. E, 2020Co-Authors: Sean D LawleyAbstract:Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations modeling subdiffusion by merely adding reaction terms to the equations describing spatial movement. A series of previous works derived fractional reaction-diffusion equations for the spatiotemporal evolution of particles undergoing subdiffusion in one space dimension with linear reactions between a finite number of discrete states. In this paper, we first give a short and elementary proof of these previous results. We then show how this argument gives the evolution equations for more general cases, including subdiffusion following any fractional Fokker-Planck equation in an arbitrary d-dimensional spatial domain with time-dependent reactions between infinitely many discrete states. In contrast to previous works which employed a variety of technical mathematical methods, our analysis reveals that the evolution equations follow from (1) the Probabilistic Independence of the stochastic spatial and discrete processes describing a single particle and (2) the linearity of the integro-differential operators describing spatial movement. We also apply our results to systems combining reactions with superdiffusion.
Bing Zhou - One of the best experts on this subject based on the ideXlab platform.
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RSKT - Naive Bayesian rough sets
Lecture Notes in Computer Science, 2010Co-Authors: Yiyu Yao, Bing ZhouAbstract:A naive Bayesian classifier is a Probabilistic classifier based on Bayesian decision theory with naive Independence assumptions, which is often used for ranking or constructing a binary classifier. The theory of rough sets provides a ternary classification method by approximating a set into positive, negative and boundary regions based on an equivalence relation on the universe. In this paper, we propose a naive Bayesian decision-theoretic rough set model, or simply a naive Bayesian rough set (NBRS) model, to integrate these two classification techniques. The conditional probability is estimated based on the Bayes' theorem and the naive Probabilistic Independence assumption. A discriminant function is defined as a monotonically increasing function of the conditional probability, which leads to analytical and computational simplifications.