It is well known that the Lasso can be interpreted as a Bayesian posterior mode estimate with a L... more It is well known that the Lasso can be interpreted as a Bayesian posterior mode estimate with a Laplacian prior. Obtaining samples from the full posterior distribution, the Bayesian Lasso, confers major advantages in performance as compared to having only the Lasso point estimate. Traditionally, the Bayesian Lasso is implemented via Gibbs sampling methods which suffer from lack of scalability, unknown convergence rates, and generation of samples that are necessarily correlated. We provide a measure transport approach to generate i.i.d samples from the posterior by constructing a transport map that transforms a sample from the Laplacian prior into a sample from the posterior. We show how the construction of this transport map can be parallelized into modules that iteratively solve Lasso problems and perform closed-form linear algebra updates. With this posterior sampling method, we perform maximum likelihood estimation of the Lasso regularization parameter via the EM algorithm. We pr...
This ground-breaking new article, "No Comemos Baterías: Solidarity Science Against False Climate Change Solutions", by the Center for Interdisciplinary Environmental Justice (CIEJ) explains why lithium batteries and electric cars exploit Indigenous peoples and threaten sacred waters in South America, how they actually create more carbon emissions that gas vehicles, and why they are not justice-centered solutions for climate change. We also define a decolonial feminist science practice and present a call to action for scientists and researchers who want to challenge capitalism and support repatriating land and life to Indigenous peoples.
The need to reason about uncertainty in large, complex, and multi-modal datasets has become incre... more The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution P to another distribution Q enables the solution to many problems in machine learning (e.g. Bayesian inference, generative modeling) and has been actively pursued from theoretical, computational, and application perspectives across the fields of information theory, computer science, and biology. Performing such transformations, in general, still leads to computational difficulties, especially in high dimensions. Here, we consider the problem of computing such "measure transport maps" with efficient and parallelizable methods. Under the mild assumptions that P need not be known but can be sampled from, and that the density of Q is known up to a proportionality constant, and that Q is log-concave, we provide in this work a convex optimization problem pertaining to relative...
The need to reason about uncertainty in large, complex, and multimodal data sets has become incre... more The need to reason about uncertainty in large, complex, and multimodal data sets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution [Formula: see text] to another distribution [Formula: see text] enables the solution to many problems in machine learning (e.g., Bayesian inference, generative modeling) and has been actively pursued from theoretical, computational, and application perspectives across the fields of information theory, computer science, and biology. Performing such transformations in general still leads to computational difficulties, especially in high dimensions. Here, we consider the problem of computing such “measure transport maps” with efficient and parallelizable methods. Under the mild assumptions that [Formula: see text] need not be known but can be sampled from and that the density of [Formula: see text] is known up to a proportionality constant, and that [Formula: see text] is log-concave...
2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2015
We present a distributed framework for finding the full posterior distribution associated with LA... more We present a distributed framework for finding the full posterior distribution associated with LASSO problems. We leverage our recent results of formulating Bayesian inference as a KL divergence minimization problem that can be solved with linear algebra updates and a series of convex point estimation problems. We show that drawing samples from the Bayesian LASSO posterior can be done by iteratively solving LASSO problems in parallel. Motivated by wearable applications where (a) the energy cost of continuous wireless transmission is prohibitive and (b) cloud storage of data induces privacy vulnerabilities, we propose a class of `analog-to-information' architectures that only transmit the minimal relevant information (e.g. the posterior) for optimal decision-making. We instantiate this result with an analog-implementable solver and show that the posterior can be calculated with systems of low-energy analog circuits in a distributed manner.
Performing inference on the Lie group of diffeomorphisms of Euclidean space has many applications... more Performing inference on the Lie group of diffeomorphisms of Euclidean space has many applications, including computer vision, computational anatomy, and density estimation. Computational tools to find such diffeomorphisms typically involve dynamical systems, and computational fluid mechanics. We here consider the problem where we are given IID samples from a distribution P and want to learn a diffeomorphism that transforms them to a samples from a known distribution Q. Using optimal transport theory, properties of relative entropy, and convex optimization, we demonstrate that when the density for Q is log-concave, efficient and scalable convex optimization algorithms can learn the diffeomorphism. We demonstrate applications in density estimation for probabilistic sleep staging where we improve classification performance.
It is well known that the Lasso can be interpreted as a Bayesian posterior mode estimate with a L... more It is well known that the Lasso can be interpreted as a Bayesian posterior mode estimate with a Laplacian prior. Obtaining samples from the full posterior distribution, the Bayesian Lasso, confers major advantages in performance as compared to having only the Lasso point estimate. Traditionally, the Bayesian Lasso is implemented via Gibbs sampling methods which suffer from lack of scalability, unknown convergence rates, and generation of samples that are necessarily correlated. We provide a measure transport approach to generate i.i.d samples from the posterior by constructing a transport map that transforms a sample from the Laplacian prior into a sample from the posterior. We show how the construction of this transport map can be parallelized into modules that iteratively solve Lasso problems and perform closed-form linear algebra updates. With this posterior sampling method, we perform maximum likelihood estimation of the Lasso regularization parameter via the EM algorithm. We pr...
This ground-breaking new article, "No Comemos Baterías: Solidarity Science Against False Climate Change Solutions", by the Center for Interdisciplinary Environmental Justice (CIEJ) explains why lithium batteries and electric cars exploit Indigenous peoples and threaten sacred waters in South America, how they actually create more carbon emissions that gas vehicles, and why they are not justice-centered solutions for climate change. We also define a decolonial feminist science practice and present a call to action for scientists and researchers who want to challenge capitalism and support repatriating land and life to Indigenous peoples.
The need to reason about uncertainty in large, complex, and multi-modal datasets has become incre... more The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution P to another distribution Q enables the solution to many problems in machine learning (e.g. Bayesian inference, generative modeling) and has been actively pursued from theoretical, computational, and application perspectives across the fields of information theory, computer science, and biology. Performing such transformations, in general, still leads to computational difficulties, especially in high dimensions. Here, we consider the problem of computing such "measure transport maps" with efficient and parallelizable methods. Under the mild assumptions that P need not be known but can be sampled from, and that the density of Q is known up to a proportionality constant, and that Q is log-concave, we provide in this work a convex optimization problem pertaining to relative...
The need to reason about uncertainty in large, complex, and multimodal data sets has become incre... more The need to reason about uncertainty in large, complex, and multimodal data sets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution [Formula: see text] to another distribution [Formula: see text] enables the solution to many problems in machine learning (e.g., Bayesian inference, generative modeling) and has been actively pursued from theoretical, computational, and application perspectives across the fields of information theory, computer science, and biology. Performing such transformations in general still leads to computational difficulties, especially in high dimensions. Here, we consider the problem of computing such “measure transport maps” with efficient and parallelizable methods. Under the mild assumptions that [Formula: see text] need not be known but can be sampled from and that the density of [Formula: see text] is known up to a proportionality constant, and that [Formula: see text] is log-concave...
2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2015
We present a distributed framework for finding the full posterior distribution associated with LA... more We present a distributed framework for finding the full posterior distribution associated with LASSO problems. We leverage our recent results of formulating Bayesian inference as a KL divergence minimization problem that can be solved with linear algebra updates and a series of convex point estimation problems. We show that drawing samples from the Bayesian LASSO posterior can be done by iteratively solving LASSO problems in parallel. Motivated by wearable applications where (a) the energy cost of continuous wireless transmission is prohibitive and (b) cloud storage of data induces privacy vulnerabilities, we propose a class of `analog-to-information' architectures that only transmit the minimal relevant information (e.g. the posterior) for optimal decision-making. We instantiate this result with an analog-implementable solver and show that the posterior can be calculated with systems of low-energy analog circuits in a distributed manner.
Performing inference on the Lie group of diffeomorphisms of Euclidean space has many applications... more Performing inference on the Lie group of diffeomorphisms of Euclidean space has many applications, including computer vision, computational anatomy, and density estimation. Computational tools to find such diffeomorphisms typically involve dynamical systems, and computational fluid mechanics. We here consider the problem where we are given IID samples from a distribution P and want to learn a diffeomorphism that transforms them to a samples from a known distribution Q. Using optimal transport theory, properties of relative entropy, and convex optimization, we demonstrate that when the density for Q is log-concave, efficient and scalable convex optimization algorithms can learn the diffeomorphism. We demonstrate applications in density estimation for probabilistic sleep staging where we improve classification performance.
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Papers by Marcela Mendoza
This ground-breaking new article, "No Comemos Baterías: Solidarity Science Against False Climate Change Solutions", by the Center for Interdisciplinary Environmental Justice (CIEJ) explains why lithium batteries and electric cars exploit Indigenous peoples and threaten sacred waters in South America, how they actually create more carbon emissions that gas vehicles, and why they are not justice-centered solutions for climate change. We also define a decolonial feminist science practice and present a call to action for scientists and researchers who want to challenge capitalism and support repatriating land and life to Indigenous peoples.
This ground-breaking new article, "No Comemos Baterías: Solidarity Science Against False Climate Change Solutions", by the Center for Interdisciplinary Environmental Justice (CIEJ) explains why lithium batteries and electric cars exploit Indigenous peoples and threaten sacred waters in South America, how they actually create more carbon emissions that gas vehicles, and why they are not justice-centered solutions for climate change. We also define a decolonial feminist science practice and present a call to action for scientists and researchers who want to challenge capitalism and support repatriating land and life to Indigenous peoples.