The Experts below are selected from a list of 28728 Experts worldwide ranked by ideXlab platform
Minghui Chen - One of the best experts on this subject based on the ideXlab platform.
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importance weighted marginal bayesian posterior Density estimation
1994Co-Authors: Minghui ChenAbstract:Abstract Markov chain sampling schemes generate dependent observations {Θi, 0 ≤ i ≤ n} from a full joint posterior distribution π(θdata). Frequently, only certain marginals of this full posterior Density are of interest; thus an interesting problem is how to estimate the marginal posterior densities based on the dependent observations {Θi, 0 ≤ i ≤ n} from π(θ data). We propose a new importance-weighted marginal Density estimation (IWMDE) method. An IWMDE is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting Conditional Density w. The asymptotic properties for the IWMDE and the guidelines for choosing a weighting Conditional Density w are also considered. A bivariate normal model and a constrained linear multiple regression model are used to illustrate how to derive the IWMDE's for the marginal posterior densities.
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importance weighted marginal bayesian posterior Density estimation
1994Co-Authors: Minghui ChenAbstract:Abstract Markov chain sampling schemes generate dependent observations {Θi, 0 ≤ i ≤ n} from a full joint posterior distribution π(θdata). Frequently, only certain marginals of this full posterior Density are of interest; thus an interesting problem is how to estimate the marginal posterior densities based on the dependent observations {Θi, 0 ≤ i ≤ n} from π(θ data). We propose a new importance-weighted marginal Density estimation (IWMDE) method. An IWMDE is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting Conditional Density w. The asymptotic properties for the IWMDE and the guidelines for choosing a weighting Conditional Density w are also considered. A bivariate normal model and a constrained linear multiple regression model are used to illustrate how to derive the IWMDE's for the marginal posterior densities.
Iain Murray - One of the best experts on this subject based on the ideXlab platform.
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fast e free inference of simulation models with bayesian Conditional Density estimation
2016Co-Authors: George Papamakarios, Iain MurrayAbstract:Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior over parameters by conditioning on data being inside an e-ball around the observed data, which is only correct in the limit e→0. Monte Carlo methods can then draw samples from the approximate posterior to approximate predictions or error bars on parameters. These algorithms critically slow down as e→0, and in practice draw samples from a broader distribution than the posterior. We propose a new approach to likelihood-free inference based on Bayesian Conditional Density estimation. Preliminary inferences based on limited simulation data are used to guide later simulations. In some cases, learning an accurate parametric representation of the entire true posterior distribution requires fewer model simulations than Monte Carlo ABC methods need to produce a single sample from an approximate posterior.
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fast epsilon free inference of simulation models with bayesian Conditional Density estimation
2016Co-Authors: George Papamakarios, Iain MurrayAbstract:Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior over parameters by conditioning on data being inside an $\epsilon$-ball around the observed data, which is only correct in the limit $\epsilon\!\rightarrow\!0$. Monte Carlo methods can then draw samples from the approximate posterior to approximate predictions or error bars on parameters. These algorithms critically slow down as $\epsilon\!\rightarrow\!0$, and in practice draw samples from a broader distribution than the posterior. We propose a new approach to likelihood-free inference based on Bayesian Conditional Density estimation. Preliminary inferences based on limited simulation data are used to guide later simulations. In some cases, learning an accurate parametric representation of the entire true posterior distribution requires fewer model simulations than Monte Carlo ABC methods need to produce a single sample from an approximate posterior.
Masashi Sugiyama - One of the best experts on this subject based on the ideXlab platform.
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Conditional Density estimation with dimensionality reduction via squared loss Conditional entropy minimization
2015Co-Authors: Voot Tangkaratt, Ning Xie, Masashi SugiyamaAbstract:Regression aims at estimating the Conditional mean of output given input. However, regression is not informative enough if the Conditional Density is multimodal, heteroskedastic, and asymmetric. In such a case, estimating the Conditional Density itself is preferable, but Conditional Density estimation (CDE) is challenging in high-dimensional space. A naive approach to coping with high dimensionality is to first perform dimensionality reduction (DR) and then execute CDE. However, a two-step process does not perform well in practice because the error incurred in the first DR step can be magnified in the second CDE step. In this letter, we propose a novel single-shot procedure that performs CDE and DR simultaneously in an integrated way. Our key idea is to formulate DR as the problem of minimizing a squared-loss variant of Conditional entropy, and this is solved using CDE. Thus, an additional CDE step is not needed after DR. We demonstrate the usefulness of the proposed method through extensive experiments on various data sets, including humanoid robot transition and computer art.
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model based policy gradients with parameter based exploration by least squares Conditional Density estimation
2014Co-Authors: Voot Tangkaratt, Syogo Mori, Tingting Zhao, Jun Morimoto, Masashi SugiyamaAbstract:The goal of reinforcement learning (RL) is to let an agent learn an optimal control policy in an unknown environment so that future expected rewards are maximized. The model-free RL approach directly learns the policy based on data samples. Although using many samples tends to improve the accuracy of policy learning, collecting a large number of samples is often expensive in practice. On the other hand, the model-based RL approach first estimates the transition model of the environment and then learns the policy based on the estimated transition model. Thus, if the transition model is accurately learned from a small amount of data, the model-based approach is a promising alternative to the model-free approach. In this paper, we propose a novel model-based RL method by combining a recently proposed model-free policy search method called policy gradients with parameter-based exploration and the state-of-the-art transition model estimator called least-squares Conditional Density estimation. Through experiments, we demonstrate the practical usefulness of the proposed method.
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Conditional Density estimation with dimensionality reduction via squared loss Conditional entropy minimization
2014Co-Authors: Voot Tangkaratt, Ning Xie, Masashi SugiyamaAbstract:Regression aims at estimating the Conditional mean of output given input. However, regression is not informative enough if the Conditional Density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the Conditional Density itself is preferable, but Conditional Density estimation (CDE) is challenging in high-dimensional space. A naive approach to coping with high-dimensionality is to first perform dimensionality reduction (DR) and then execute CDE. However, such a two-step process does not perform well in practice because the error incurred in the first DR step can be magnified in the second CDE step. In this paper, we propose a novel single-shot procedure that performs CDE and DR simultaneously in an integrated way. Our key idea is to formulate DR as the problem of minimizing a squared-loss variant of Conditional entropy, and this is solved via CDE. Thus, an additional CDE step is not needed after DR. We demonstrate the usefulness of the proposed method through extensive experiments on various datasets including humanoid robot transition and computer art.
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Conditional Density estimation via least squares Density ratio estimation
2010Co-Authors: Masashi Sugiyama, Taiji Suzuki, Takafumi Kanamori, Hirotaka Hachiya, Ichiro Takeuchi, Daisuke OkanoharaAbstract:Estimating the Conditional mean of an inputoutput relation is the goal of regression. However, regression analysis is not sufficiently informative if the Conditional distribution has multi-modality, is highly asymmetric, or contains heteroscedastic noise. In such scenarios, estimating the Conditional distribution itself would be more useful. In this paper, we propose a novel method of Conditional Density estimation. Our basic idea is to express the Conditional Density in terms of the ratio of unConditional densities, and the ratio is directly estimated without going through Density estimation. Experiments using benchmark and robot transition datasets illustrate the usefulness of the proposed approach.
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Least-Squares Conditional Density Estimation
2010Co-Authors: Masashi Sugiyama, Taiji Suzuki, Takafumi Kanamori, Hirotaka Hachiya, Ichiro Takeuchi, Daisuke OkanoharaAbstract:Estimating the Conditional mean of an input-output relation is the goal of regression. However, regression analysis is not sufficiently informative if the Conditional distribution has multi-modality, is highly asymmetric, or contains heteroscedastic noise. In such scenarios, estimating the Conditional distribution itself would be more useful. In this paper, we propose a novel method of Conditional Density estimation that is suitable for multi-dimensional continuous variables. The basic idea of the proposed method is to express the Conditional Density in terms of the Density ratio and the ratio is directly estimated without going through Density estimation. Experiments using benchmark and robot transition datasets illustrate the usefulness of the proposed approach.
Ann B Lee - One of the best experts on this subject based on the ideXlab platform.
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diagnostics for Conditional Density models and bayesian inference algorithms
2021Co-Authors: David Zhao, Niccolo Dalmasso, Rafael Izbicki, Ann B LeeAbstract:There has been growing interest in the AI community for precise uncertainty quantification. Conditional Density models f(y|x), where x represents potentially high-dimensional features, are an integral part of uncertainty quantification in prediction and Bayesian inference. However, it is challenging to assess Conditional Density estimates and gain insight into modes of failure. While existing diagnostic tools can determine whether an approximated Conditional Density is compatible overall with a data sample, they lack a principled framework for identifying, locating, and interpreting the nature of statistically significant discrepancies over the entire feature space. In this paper, we present rigorous and easy-to-interpret diagnostics such as (i) the "Local Coverage Test" (LCT), which distinguishes an arbitrarily misspecified model from the true Conditional Density of the sample, and (ii) "Amortized Local P-P plots" (ALP) which can quickly provide interpretable graphical summaries of distributional differences at any location x in the feature space. Our validation procedures scale to high dimensions and can potentially adapt to any type of data at hand. We demonstrate the effectiveness of LCT and ALP through a simulated experiment and applications to prediction and parameter inference for image data.
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Conditional Density estimation tools in python and r with applications to photometric redshifts and likelihood free cosmological inference
2020Co-Authors: Niccolo Dalmasso, Rafael Izbicki, Ann B Lee, Taylor Pospisil, Peter E Freeman, A I MalzAbstract:Abstract It is well known in astronomy that propagating non-Gaussian prediction uncertainty in photometric redshift estimates is key to reducing bias in downstream cosmological analyses. Similarly, likelihood-free inference approaches, which are beginning to emerge as a tool for cosmological analysis, require a characterization of the full uncertainty landscape of the parameters of interest given observed data. However, most machine learning (ML) or training-based methods with open-source software target point prediction or classification, and hence fall short in quantifying uncertainty in complex regression and parameter inference settings such as the applications mentioned above. As an alternative to methods that focus on predicting the response (or parameters) y from features x , we provide nonparametric Conditional Density estimation (CDE) tools for approximating and validating the entire probability Density function (PDF) p ( y | x ) of y given (i.e., Conditional on) x . This Density approach offers a more nuanced accounting of uncertainty in situations with, e.g., nonstandard error distributions and multimodal or heteroskedastic response variables that are often present in astronomical data sets. As there is no one-size-fits-all CDE method, and the ultimate choice of model depends on the application and the training sample size, the goal of this work is to provide a comprehensive range of statistical tools and open-source software for nonparametric CDE and method assessment which can accommodate different types of settings – involving, e.g., mixed-type input from multiple sources, functional data, and images – and which in addition can easily be fit to the problem at hand. Specifically, we introduce four CDE software packages in Python and R based on ML prediction methods adapted and optimized for CDE: NNKCDE , RFCDE , FlexCode , and DeepCDE . Furthermore, we present the cdetools package with evaluation metrics. This package includes functions for computing a CDE loss function for tuning and assessing the quality of individual PDFs, together with diagnostic functions that probe the population-level performance of the PDFs. We provide sample code in Python and R as well as examples of applications to photometric redshift estimation and likelihood-free cosmological inference via CDE.
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Conditional Density estimation tools in python and r with applications to photometric redshifts and likelihood free cosmological inference
2019Co-Authors: Niccolo Dalmasso, Rafael Izbicki, Ann B Lee, Taylor Pospisil, Peter E Freeman, A I MalzAbstract:It is well known in astronomy that propagating non-Gaussian prediction uncertainty in photometric redshift estimates is key to reducing bias in downstream cosmological analyses. Similarly, likelihood-free inference approaches, which are beginning to emerge as a tool for cosmological analysis, require a characterization of the full uncertainty landscape of the parameters of interest given observed data. However, most machine learning (ML) or training-based methods with open-source software target point prediction or classification, and hence fall short in quantifying uncertainty in complex regression and parameter inference settings. As an alternative to methods that focus on predicting the response (or parameters) $\mathbf{y}$ from features $\mathbf{x}$, we provide nonparametric Conditional Density estimation (CDE) tools for approximating and validating the entire probability Density function (PDF) $\mathrm{p}(\mathbf{y}|\mathbf{x})$ of $\mathbf{y}$ given (i.e., Conditional on) $\mathbf{x}$. As there is no one-size-fits-all CDE method, the goal of this work is to provide a comprehensive range of statistical tools and open-source software for nonparametric CDE and method assessment which can accommodate different types of settings and be easily fit to the problem at hand. Specifically, we introduce four CDE software packages in $\texttt{Python}$ and $\texttt{R}$ based on ML prediction methods adapted and optimized for CDE: $\texttt{NNKCDE}$, $\texttt{RFCDE}$, $\texttt{FlexCode}$, and $\texttt{DeepCDE}$. Furthermore, we present the $\texttt{cdetools}$ package, which includes functions for computing a CDE loss function for tuning and assessing the quality of individual PDFs, along with diagnostic functions. We provide sample code in $\texttt{Python}$ and $\texttt{R}$ as well as examples of applications to photometric redshift estimation and likelihood-free cosmological inference via CDE.
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Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation
2017Co-Authors: Rafael Izbicki, Ann B LeeAbstract:There is a growing demand for nonparametric Conditional Density estimators (CDEs) in fields such as astronomy and economics. In astronomy, for example, one can dramatically improve estimates of the parameters that dictate the evolution of the Universe by working with full Conditional densities instead of regression (i.e., Conditional mean) estimates. More generally, standard regression falls short in any prediction problem where the distribution of the response is more complex with multi-modality, asymmetry or heteroscedastic noise. Nevertheless, much of the work on high-dimensional inference concerns regression and classification only, whereas research on Density estimation has lagged behind. Here we propose FlexCode, a fully nonparametric approach to Conditional Density estimation that reformulates CDE as a non-parametric orthogonal series problem where the expansion coefficients are estimated by regression. By taking such an approach, one can efficiently estimate Conditional densities and not just expectations in high dimensions by drawing upon the success in high-dimensional regression. Depending on the choice of regression procedure, our method can adapt to a variety of challenging high-dimensional settings with different structures in the data (e.g., a large number of irrelevant components and nonlinear manifold structure) as well as different data types (e.g., functional data, mixed data types and sample sets). We study the theoretical and empirical performance of our proposed method, and we compare our approach with traditional Conditional Density estimators on simulated as well as real-world data, such as photometric galaxy data, Twitter data, and line-of-sight velocities in a galaxy cluster.
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nonparametric Conditional Density estimation in a high dimensional regression setting
2016Co-Authors: Rafael Izbicki, Ann B LeeAbstract:In some applications (e.g., in cosmology and economics), the regression E[Z|x] is not adequate to represent the association between a predictor x and a response Z because of multi-modality and asymmetry of f(z|x); using the full Density instead of a single-point estimate can then lead to less bias in subsequent analysis. As of now, there are no effective ways of estimating f(z|x) when x represents high-dimensional, complex data. In this article, we propose a new nonparametric estimator of f(z|x) that adapts to sparse (low-dimensional) structure in x. By directly expanding f(z|x) in the eigenfunctions of a kernel-based operator, we avoid tensor products in high dimensions as well as ratios of estimated densities. Our basis functions are orthogonal with respect to the underlying data distribution, allowing fast implementation and tuning of parameters. We derive rates of convergence and show that the method adapts to the intrinsic dimension of the data. We also demonstrate the effectiveness of the series met...
Niccolo Dalmasso - One of the best experts on this subject based on the ideXlab platform.
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diagnostics for Conditional Density models and bayesian inference algorithms
2021Co-Authors: David Zhao, Niccolo Dalmasso, Rafael Izbicki, Ann B LeeAbstract:There has been growing interest in the AI community for precise uncertainty quantification. Conditional Density models f(y|x), where x represents potentially high-dimensional features, are an integral part of uncertainty quantification in prediction and Bayesian inference. However, it is challenging to assess Conditional Density estimates and gain insight into modes of failure. While existing diagnostic tools can determine whether an approximated Conditional Density is compatible overall with a data sample, they lack a principled framework for identifying, locating, and interpreting the nature of statistically significant discrepancies over the entire feature space. In this paper, we present rigorous and easy-to-interpret diagnostics such as (i) the "Local Coverage Test" (LCT), which distinguishes an arbitrarily misspecified model from the true Conditional Density of the sample, and (ii) "Amortized Local P-P plots" (ALP) which can quickly provide interpretable graphical summaries of distributional differences at any location x in the feature space. Our validation procedures scale to high dimensions and can potentially adapt to any type of data at hand. We demonstrate the effectiveness of LCT and ALP through a simulated experiment and applications to prediction and parameter inference for image data.
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Conditional Density estimation tools in python and r with applications to photometric redshifts and likelihood free cosmological inference
2020Co-Authors: Niccolo Dalmasso, Rafael Izbicki, Ann B Lee, Taylor Pospisil, Peter E Freeman, A I MalzAbstract:Abstract It is well known in astronomy that propagating non-Gaussian prediction uncertainty in photometric redshift estimates is key to reducing bias in downstream cosmological analyses. Similarly, likelihood-free inference approaches, which are beginning to emerge as a tool for cosmological analysis, require a characterization of the full uncertainty landscape of the parameters of interest given observed data. However, most machine learning (ML) or training-based methods with open-source software target point prediction or classification, and hence fall short in quantifying uncertainty in complex regression and parameter inference settings such as the applications mentioned above. As an alternative to methods that focus on predicting the response (or parameters) y from features x , we provide nonparametric Conditional Density estimation (CDE) tools for approximating and validating the entire probability Density function (PDF) p ( y | x ) of y given (i.e., Conditional on) x . This Density approach offers a more nuanced accounting of uncertainty in situations with, e.g., nonstandard error distributions and multimodal or heteroskedastic response variables that are often present in astronomical data sets. As there is no one-size-fits-all CDE method, and the ultimate choice of model depends on the application and the training sample size, the goal of this work is to provide a comprehensive range of statistical tools and open-source software for nonparametric CDE and method assessment which can accommodate different types of settings – involving, e.g., mixed-type input from multiple sources, functional data, and images – and which in addition can easily be fit to the problem at hand. Specifically, we introduce four CDE software packages in Python and R based on ML prediction methods adapted and optimized for CDE: NNKCDE , RFCDE , FlexCode , and DeepCDE . Furthermore, we present the cdetools package with evaluation metrics. This package includes functions for computing a CDE loss function for tuning and assessing the quality of individual PDFs, together with diagnostic functions that probe the population-level performance of the PDFs. We provide sample code in Python and R as well as examples of applications to photometric redshift estimation and likelihood-free cosmological inference via CDE.
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Conditional Density estimation tools in python and r with applications to photometric redshifts and likelihood free cosmological inference
2019Co-Authors: Niccolo Dalmasso, Rafael Izbicki, Ann B Lee, Taylor Pospisil, Peter E Freeman, A I MalzAbstract:It is well known in astronomy that propagating non-Gaussian prediction uncertainty in photometric redshift estimates is key to reducing bias in downstream cosmological analyses. Similarly, likelihood-free inference approaches, which are beginning to emerge as a tool for cosmological analysis, require a characterization of the full uncertainty landscape of the parameters of interest given observed data. However, most machine learning (ML) or training-based methods with open-source software target point prediction or classification, and hence fall short in quantifying uncertainty in complex regression and parameter inference settings. As an alternative to methods that focus on predicting the response (or parameters) $\mathbf{y}$ from features $\mathbf{x}$, we provide nonparametric Conditional Density estimation (CDE) tools for approximating and validating the entire probability Density function (PDF) $\mathrm{p}(\mathbf{y}|\mathbf{x})$ of $\mathbf{y}$ given (i.e., Conditional on) $\mathbf{x}$. As there is no one-size-fits-all CDE method, the goal of this work is to provide a comprehensive range of statistical tools and open-source software for nonparametric CDE and method assessment which can accommodate different types of settings and be easily fit to the problem at hand. Specifically, we introduce four CDE software packages in $\texttt{Python}$ and $\texttt{R}$ based on ML prediction methods adapted and optimized for CDE: $\texttt{NNKCDE}$, $\texttt{RFCDE}$, $\texttt{FlexCode}$, and $\texttt{DeepCDE}$. Furthermore, we present the $\texttt{cdetools}$ package, which includes functions for computing a CDE loss function for tuning and assessing the quality of individual PDFs, along with diagnostic functions. We provide sample code in $\texttt{Python}$ and $\texttt{R}$ as well as examples of applications to photometric redshift estimation and likelihood-free cosmological inference via CDE.