Filtering is a general name for inferring the states of a dynamical system given observations. Th... more Filtering is a general name for inferring the states of a dynamical system given observations. The most common filtering approach is Gaussian Filtering (GF) where the distribution of the inferred states is a Gaussian whose mean is an affine function of the observations. There are two restrictions in this model: Gaussianity and Affinity. We propose a model to relax both these assumptions based on recent advances in implicit generative models. Empirical results show that the proposed method gives a significant advantage over GF and nonlinear methods based on fixed nonlinear kernels.
international conference on machine learning, Jul 3, 2018
Generative adversarial networks (GANs) have been shown to produce realistic samples from high-dim... more Generative adversarial networks (GANs) have been shown to produce realistic samples from high-dimensional distributions, but training them is considered hard. A possible explanation for training instabilities is the inherent imbalance between the networks: While the discriminator is trained directly on both real and fake samples, the generator only has control over the fake samples it produces since the real data distribution is fixed by the choice of a given dataset. We propose a simple modification that gives the generator control over the real samples which leads to a tempered learning process for both generator and discriminator. The real data distribution passes through a lens before being revealed to the discriminator, balancing the generator and discriminator by gradually revealing more detailed features necessary to produce high-quality results. The proposed module automatically adjusts the learning process to the current strength of the networks, yet is generic and easy to add to any GAN variant. In a number of experiments, we show that this can improve quality, stability and/or convergence speed across a range of different GAN architectures (DCGAN, LSGAN, WGAN-GP).
Model-free and model-based reinforcement learning are two ends of a spectrum. Learning a good pol... more Model-free and model-based reinforcement learning are two ends of a spectrum. Learning a good policy without a dynamic model can be prohibitively expensive. Learning the dynamic model of a system can reduce the cost of learning the policy, but it can also introduce bias if it is not accurate. We propose a middle ground where instead of the transition model, the sensitivity of the trajectories with respect to the perturbation of the parameters is learned. This allows us to predict the local behavior of the physical system around a set of nominal policies without knowing the actual model. We assay our method on a custom-built physical robot in extensive experiments and show the feasibility of the approach in practice. We investigate potential challenges when applying our method to physical systems and propose solutions to each of them.
Generative adversarial networks are used to generate images but still their convergence propertie... more Generative adversarial networks are used to generate images but still their convergence properties are not well understood. There have been a few studies who intended to investigate the stability properties of GANs as a dynamical system. This short writing can be seen in that direction. Among the proposed methods for stabilizing training of GANs, ß-GAN was the first who proposed a complete annealing strategy to change high-level conditions of the GAN objective. In this note, we show by a simple example how annealing strategy works in GANs. The theoretical analysis is supported by simple simulations.
Score-based methods represented as stochastic differential equations on a continuous time domain ... more Score-based methods represented as stochastic differential equations on a continuous time domain have recently proven successful as a non-adversarial generative model. Training such models relies on denoising score matching, which can be seen as multi-scale denoising autoencoders. Here, we augment the denoising scorematching framework to enable representation learning without any supervised signal. GANs and VAEs learn representations by directly transforming latent codes to data samples. In contrast, the introduced diffusion-based representation learning relies on a new formulation of the denoising score-matching objective and thus encodes information needed for denoising. We illustrate how this difference allows for manual control of the level of details encoded in the representation. Using the same approach, we propose to learn an infinite-dimensional latent code which achieves improvements of state-of-the-art models on semi-supervised image classification. As a side contribution,...
Generative adversarial networks are used to generate images but still their convergence propertie... more Generative adversarial networks are used to generate images but still their convergence properties are not well understood. There have been a few studies who intended to investigate the stability properties of GANs as a dynamical system. This short writing can be seen in that direction. Among the proposed methods for stabilizing training of GANs, {\ss}-GAN was the first who proposed a complete annealing strategy to change high-level conditions of the GAN objective. In this note, we show by a simple example how annealing strategy works in GANs. The theoretical analysis is supported by simple simulations.
Learning controllers merely based on a performance metric has been proven effective in many physi... more Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion of safety to ensure that it does not harm either the agent or the environment. Stability is a crucial notion of safety, whose violation can certainly cause unsafe behaviors. Lyapunov functions are effective tools to assess stability in nonlinear dynamical systems. In this paper, we combine an improving Lyapunov function with automatic controller synthesis to obtain control policies with large safe regions. We propose a two-player collaborative algorithm that alternates between estimating a Lyapunov function and deriving a controller that gradually enlarges the stability region of the closed-loop system. We provide theoretical results on the class of systems that can be treated with the proposed algorithm and empirically evaluate the effectiveness o...
Representation Learning in Continuous-Time Score-Based Generative Models
ArXiv, 2021
Score-based methods represented as stochastic differential equations on a continuous time domain ... more Score-based methods represented as stochastic differential equations on a continuous time domain have recently proven successful as a non-adversarial generative model. Training such models relies on denoising score matching, which can be seen as multi-scale denoising autoencoders. Here, we augment the denoising score-matching framework to enable representation learning without any supervised signal. GANs and VAEs learn representations by directly transforming latent codes to data samples. In contrast, score-based representation learning relies on a new formulation of the denoising score-matching objective and thus encodes information needed for denoising. We show how this difference allows for manual control of the level of detail encoded in the representation. 1 SCORE-BASED GENERATIVE MODELING Score-based methods have recently proven successful for generating images Song & Ermon (2020); Song et al. (2020), graphs Niu et al. (2020), shapes Cai et al. (2020), and audio Chen et al. (2...
Generative adversarial networks are used to generate images but still their convergence propertie... more Generative adversarial networks are used to generate images but still their convergence properties are not well understood. There have been a few studies who intended to investigate the stability properties of GANs as a dynamical system. This paper can be seen in that direction. Among the proposed methods for stabilizing training of GANs, some of them modify the data distribution during the course of training. We unify these methods under the name nonautonomous GAN and investigate their dynamical behaviour when the data distribution is not stationary. We provide theoretical analysis which is supported by simple simulations along with experiments on high dimensional datasets.
We introduce a novel framework for adversarial training where the target distribution is annealed... more We introduce a novel framework for adversarial training where the target distribution is annealed between the uniform distribution and the data distribution. We posited a conjecture that learning under continuous annealing in the nonparametric regime is stable irrespective of the divergence measures in the objective function and proposed an algorithm, dubbed {\ss}-GAN, in corollary. In this framework, the fact that the initial support of the generative network is the whole ambient space combined with annealing are key to balancing the minimax game. In our experiments on synthetic data, MNIST, and CelebA, {\ss}-GAN with a fixed annealing schedule was stable and did not suffer from mode collapse.
Humans show an innate ability to learn the regularities of the world through interaction. By perf... more Humans show an innate ability to learn the regularities of the world through interaction. By performing experiments in our environment, we are able to discern the causal factors of variation and infer how they affect the dynamics of our world. Analogously, here we attempt to equip reinforcement learning agents with the ability to perform experiments that facilitate a categorization of the rolled-out trajectories, and to subsequently infer the causal factors of the environment in a hierarchical manner. We introduce a novel intrinsic reward, called causal curiosity, and show that it allows our agents to learn optimal sequences of actions, and to discover causal factors in the dynamics. The learned behavior allows the agent to infer a binary quantized representation for the ground-truth causal factors in every environment. Additionally, we find that these experimental behaviors are semantically meaningful (e.g., to differentiate between heavy and light blocks, our agents learn to lift ...
We consider the problem of recovering a common latent source with independent components from mul... more We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy ...
We present a novel algorithm for instrumental variable (IV) regression, DualIV, which simplifies ... more We present a novel algorithm for instrumental variable (IV) regression, DualIV, which simplifies traditional two-stage methods via a dual formulation. Inspired by problems in stochastic programming, we show that the two-stage procedure for nonlinear IV regression can be reformulated as a convex-concave saddle-point problem. Our formulation circumvents the first-stage regression which is a potential bottleneck in real-world applications. Based on this new approach, we develop a simple kernel-based algorithm with a closed-form solution. Empirical results show that we are competitive to existing, more complicated algorithms for instrumental variable regression.
Malaria is a serious infectious disease that is responsible for over half million deaths yearly w... more Malaria is a serious infectious disease that is responsible for over half million deaths yearly worldwide. The major cause of these mortalities is late or inaccurate diagnosis. Manual microscopy is currently considered as the dominant diagnostic method for malaria. However, it is time consuming and prone to human errors. The aim of this paper is to automate the diagnosis process and minimize the human intervention. We have developed the hardware and software for a cost-efficient malaria diagnostic system. This paper describes the manufactured hardware and also proposes novel software to handle parasite detection and life-stage identification. A motorized microscope is developed to take images from Giemsa-stained blood smears. A patch-based unsupervised statistical clustering algorithm is proposed which offers a novel method for classification of different regions within blood images. The proposed method provides better robustness against different imaging settings. The core of the p...
Minimum Information Exchange in Distributed Systems
ArXiv, 2018
Efficient representation of observed data has many applications in various domains of engineering... more Efficient representation of observed data has many applications in various domains of engineering and science. Having a good representation of data, downstream tasks such as classification, regression, and decision making become easier. Even though representing still datasets such as images is a living branch in machine learning, representation of dynamical systems has received less attention. One area where such representation is beneficial is distributed control systems. Distributed systems can be modeled as graphs consisting of nodes that exchange information. This exchange is often costly (e.g. when happening over a shared network) and thus needs to be minimized, while a predefined objective is still satisfied. In this work, we present a method to represent a dynamical system efficiently as a combination of state and local approximate model to fulfill a criterion similar to Minimum Description Length (MDL) principle. MDL is used in machine learning and statistics to state that t...
Discriminative learning machines often need a large set of labeled samples for training. Active l... more Discriminative learning machines often need a large set of labeled samples for training. Active learning (AL) settings assume that the learner has the freedom to ask an oracle to label its desired samples. Traditional AL algorithms heuristically choose query samples about which the current learner is uncertain. This strategy does not make good use of the structure of the dataset at hand and is prone to be misguided by outliers. To alleviate this problem, we propose to distill the structural information into a probabilistic generative model which acts as a \emph{teacher} in our model. The active \emph{learner} uses this information effectively at each cycle of active learning. The proposed method is generic and does not depend on the type of learner and teacher. We then suggest a query criterion for active learning that is aware of distribution of data and is more robust against outliers. Our method can be combined readily with several other query criteria for active learning. We pro...
A coupled computational approach to simultaneously learn a vector field and the region of attract... more A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability information as a prior on the system, effectively endowing the estimate with this important structural property. In addition, the knowledge of the region of attraction plays an experiment design role by informing the selection of initial conditions from which trajectories are generated and by enabling the use of a Lyapunov function of the system as a regularization term. Numerical results show that the proposed method allows efficient sampling and provides an accurate estimate of the dynamics in an inner approximation of its region of attraction.
We present a novel single-stage procedure for instrumental variable (IV) regression called DualIV... more We present a novel single-stage procedure for instrumental variable (IV) regression called DualIV which simplifies traditional two-stage regression via a dual formulation. We show that the common two-stage procedure can alternatively be solved via generalized least squares. Our formulation circumvents the first-stage regression which can be a bottleneck in modern two-stage procedures for IV regression. We also show that our framework is closely related to the generalized method of moments (GMM) with specific assumptions. This highlights the fundamental connection between GMM and two-stage procedures in IV literature. Using the proposed framework, we develop a simple kernel-based algorithm with consistency guarantees. Lastly, we give empirical results illustrating the advantages of our method over the existing two-stage algorithms.
Simulating the spread of infectious diseases in human communities is critical for predicting the ... more Simulating the spread of infectious diseases in human communities is critical for predicting the trajectory of an epidemic and verifying various policies to control the devastating impacts of the outbreak. Many existing simulators are based on compartment models that divide people into a few subsets and simulate the dynamics among those subsets using hypothesized differential equations. However, these models lack the requisite granularity to study the effect of intelligent policies that influence every individual in a particular way. In this work, we introduce a simulator software capable of modeling a population structure and controlling the disease’s propagation at an individualistic level. In order to estimate the confidence of the conclusions drawn from the simulator, we employ a comprehensive probabilistic approach where the entire population is constructed as a hierarchical random variable. This approach makes the inferred conclusions more robust against sampling artifacts and...
Filtering is a general name for inferring the states of a dynamical system given observations. Th... more Filtering is a general name for inferring the states of a dynamical system given observations. The most common filtering approach is Gaussian Filtering (GF) where the distribution of the inferred states is a Gaussian whose mean is an affine function of the observations. There are two restrictions in this model: Gaussianity and Affinity. We propose a model to relax both these assumptions based on recent advances in implicit generative models. Empirical results show that the proposed method gives a significant advantage over GF and nonlinear methods based on fixed nonlinear kernels.
international conference on machine learning, Jul 3, 2018
Generative adversarial networks (GANs) have been shown to produce realistic samples from high-dim... more Generative adversarial networks (GANs) have been shown to produce realistic samples from high-dimensional distributions, but training them is considered hard. A possible explanation for training instabilities is the inherent imbalance between the networks: While the discriminator is trained directly on both real and fake samples, the generator only has control over the fake samples it produces since the real data distribution is fixed by the choice of a given dataset. We propose a simple modification that gives the generator control over the real samples which leads to a tempered learning process for both generator and discriminator. The real data distribution passes through a lens before being revealed to the discriminator, balancing the generator and discriminator by gradually revealing more detailed features necessary to produce high-quality results. The proposed module automatically adjusts the learning process to the current strength of the networks, yet is generic and easy to add to any GAN variant. In a number of experiments, we show that this can improve quality, stability and/or convergence speed across a range of different GAN architectures (DCGAN, LSGAN, WGAN-GP).
Model-free and model-based reinforcement learning are two ends of a spectrum. Learning a good pol... more Model-free and model-based reinforcement learning are two ends of a spectrum. Learning a good policy without a dynamic model can be prohibitively expensive. Learning the dynamic model of a system can reduce the cost of learning the policy, but it can also introduce bias if it is not accurate. We propose a middle ground where instead of the transition model, the sensitivity of the trajectories with respect to the perturbation of the parameters is learned. This allows us to predict the local behavior of the physical system around a set of nominal policies without knowing the actual model. We assay our method on a custom-built physical robot in extensive experiments and show the feasibility of the approach in practice. We investigate potential challenges when applying our method to physical systems and propose solutions to each of them.
Generative adversarial networks are used to generate images but still their convergence propertie... more Generative adversarial networks are used to generate images but still their convergence properties are not well understood. There have been a few studies who intended to investigate the stability properties of GANs as a dynamical system. This short writing can be seen in that direction. Among the proposed methods for stabilizing training of GANs, ß-GAN was the first who proposed a complete annealing strategy to change high-level conditions of the GAN objective. In this note, we show by a simple example how annealing strategy works in GANs. The theoretical analysis is supported by simple simulations.
Score-based methods represented as stochastic differential equations on a continuous time domain ... more Score-based methods represented as stochastic differential equations on a continuous time domain have recently proven successful as a non-adversarial generative model. Training such models relies on denoising score matching, which can be seen as multi-scale denoising autoencoders. Here, we augment the denoising scorematching framework to enable representation learning without any supervised signal. GANs and VAEs learn representations by directly transforming latent codes to data samples. In contrast, the introduced diffusion-based representation learning relies on a new formulation of the denoising score-matching objective and thus encodes information needed for denoising. We illustrate how this difference allows for manual control of the level of details encoded in the representation. Using the same approach, we propose to learn an infinite-dimensional latent code which achieves improvements of state-of-the-art models on semi-supervised image classification. As a side contribution,...
Generative adversarial networks are used to generate images but still their convergence propertie... more Generative adversarial networks are used to generate images but still their convergence properties are not well understood. There have been a few studies who intended to investigate the stability properties of GANs as a dynamical system. This short writing can be seen in that direction. Among the proposed methods for stabilizing training of GANs, {\ss}-GAN was the first who proposed a complete annealing strategy to change high-level conditions of the GAN objective. In this note, we show by a simple example how annealing strategy works in GANs. The theoretical analysis is supported by simple simulations.
Learning controllers merely based on a performance metric has been proven effective in many physi... more Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion of safety to ensure that it does not harm either the agent or the environment. Stability is a crucial notion of safety, whose violation can certainly cause unsafe behaviors. Lyapunov functions are effective tools to assess stability in nonlinear dynamical systems. In this paper, we combine an improving Lyapunov function with automatic controller synthesis to obtain control policies with large safe regions. We propose a two-player collaborative algorithm that alternates between estimating a Lyapunov function and deriving a controller that gradually enlarges the stability region of the closed-loop system. We provide theoretical results on the class of systems that can be treated with the proposed algorithm and empirically evaluate the effectiveness o...
Representation Learning in Continuous-Time Score-Based Generative Models
ArXiv, 2021
Score-based methods represented as stochastic differential equations on a continuous time domain ... more Score-based methods represented as stochastic differential equations on a continuous time domain have recently proven successful as a non-adversarial generative model. Training such models relies on denoising score matching, which can be seen as multi-scale denoising autoencoders. Here, we augment the denoising score-matching framework to enable representation learning without any supervised signal. GANs and VAEs learn representations by directly transforming latent codes to data samples. In contrast, score-based representation learning relies on a new formulation of the denoising score-matching objective and thus encodes information needed for denoising. We show how this difference allows for manual control of the level of detail encoded in the representation. 1 SCORE-BASED GENERATIVE MODELING Score-based methods have recently proven successful for generating images Song & Ermon (2020); Song et al. (2020), graphs Niu et al. (2020), shapes Cai et al. (2020), and audio Chen et al. (2...
Generative adversarial networks are used to generate images but still their convergence propertie... more Generative adversarial networks are used to generate images but still their convergence properties are not well understood. There have been a few studies who intended to investigate the stability properties of GANs as a dynamical system. This paper can be seen in that direction. Among the proposed methods for stabilizing training of GANs, some of them modify the data distribution during the course of training. We unify these methods under the name nonautonomous GAN and investigate their dynamical behaviour when the data distribution is not stationary. We provide theoretical analysis which is supported by simple simulations along with experiments on high dimensional datasets.
We introduce a novel framework for adversarial training where the target distribution is annealed... more We introduce a novel framework for adversarial training where the target distribution is annealed between the uniform distribution and the data distribution. We posited a conjecture that learning under continuous annealing in the nonparametric regime is stable irrespective of the divergence measures in the objective function and proposed an algorithm, dubbed {\ss}-GAN, in corollary. In this framework, the fact that the initial support of the generative network is the whole ambient space combined with annealing are key to balancing the minimax game. In our experiments on synthetic data, MNIST, and CelebA, {\ss}-GAN with a fixed annealing schedule was stable and did not suffer from mode collapse.
Humans show an innate ability to learn the regularities of the world through interaction. By perf... more Humans show an innate ability to learn the regularities of the world through interaction. By performing experiments in our environment, we are able to discern the causal factors of variation and infer how they affect the dynamics of our world. Analogously, here we attempt to equip reinforcement learning agents with the ability to perform experiments that facilitate a categorization of the rolled-out trajectories, and to subsequently infer the causal factors of the environment in a hierarchical manner. We introduce a novel intrinsic reward, called causal curiosity, and show that it allows our agents to learn optimal sequences of actions, and to discover causal factors in the dynamics. The learned behavior allows the agent to infer a binary quantized representation for the ground-truth causal factors in every environment. Additionally, we find that these experimental behaviors are semantically meaningful (e.g., to differentiate between heavy and light blocks, our agents learn to lift ...
We consider the problem of recovering a common latent source with independent components from mul... more We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy ...
We present a novel algorithm for instrumental variable (IV) regression, DualIV, which simplifies ... more We present a novel algorithm for instrumental variable (IV) regression, DualIV, which simplifies traditional two-stage methods via a dual formulation. Inspired by problems in stochastic programming, we show that the two-stage procedure for nonlinear IV regression can be reformulated as a convex-concave saddle-point problem. Our formulation circumvents the first-stage regression which is a potential bottleneck in real-world applications. Based on this new approach, we develop a simple kernel-based algorithm with a closed-form solution. Empirical results show that we are competitive to existing, more complicated algorithms for instrumental variable regression.
Malaria is a serious infectious disease that is responsible for over half million deaths yearly w... more Malaria is a serious infectious disease that is responsible for over half million deaths yearly worldwide. The major cause of these mortalities is late or inaccurate diagnosis. Manual microscopy is currently considered as the dominant diagnostic method for malaria. However, it is time consuming and prone to human errors. The aim of this paper is to automate the diagnosis process and minimize the human intervention. We have developed the hardware and software for a cost-efficient malaria diagnostic system. This paper describes the manufactured hardware and also proposes novel software to handle parasite detection and life-stage identification. A motorized microscope is developed to take images from Giemsa-stained blood smears. A patch-based unsupervised statistical clustering algorithm is proposed which offers a novel method for classification of different regions within blood images. The proposed method provides better robustness against different imaging settings. The core of the p...
Minimum Information Exchange in Distributed Systems
ArXiv, 2018
Efficient representation of observed data has many applications in various domains of engineering... more Efficient representation of observed data has many applications in various domains of engineering and science. Having a good representation of data, downstream tasks such as classification, regression, and decision making become easier. Even though representing still datasets such as images is a living branch in machine learning, representation of dynamical systems has received less attention. One area where such representation is beneficial is distributed control systems. Distributed systems can be modeled as graphs consisting of nodes that exchange information. This exchange is often costly (e.g. when happening over a shared network) and thus needs to be minimized, while a predefined objective is still satisfied. In this work, we present a method to represent a dynamical system efficiently as a combination of state and local approximate model to fulfill a criterion similar to Minimum Description Length (MDL) principle. MDL is used in machine learning and statistics to state that t...
Discriminative learning machines often need a large set of labeled samples for training. Active l... more Discriminative learning machines often need a large set of labeled samples for training. Active learning (AL) settings assume that the learner has the freedom to ask an oracle to label its desired samples. Traditional AL algorithms heuristically choose query samples about which the current learner is uncertain. This strategy does not make good use of the structure of the dataset at hand and is prone to be misguided by outliers. To alleviate this problem, we propose to distill the structural information into a probabilistic generative model which acts as a \emph{teacher} in our model. The active \emph{learner} uses this information effectively at each cycle of active learning. The proposed method is generic and does not depend on the type of learner and teacher. We then suggest a query criterion for active learning that is aware of distribution of data and is more robust against outliers. Our method can be combined readily with several other query criteria for active learning. We pro...
A coupled computational approach to simultaneously learn a vector field and the region of attract... more A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability information as a prior on the system, effectively endowing the estimate with this important structural property. In addition, the knowledge of the region of attraction plays an experiment design role by informing the selection of initial conditions from which trajectories are generated and by enabling the use of a Lyapunov function of the system as a regularization term. Numerical results show that the proposed method allows efficient sampling and provides an accurate estimate of the dynamics in an inner approximation of its region of attraction.
We present a novel single-stage procedure for instrumental variable (IV) regression called DualIV... more We present a novel single-stage procedure for instrumental variable (IV) regression called DualIV which simplifies traditional two-stage regression via a dual formulation. We show that the common two-stage procedure can alternatively be solved via generalized least squares. Our formulation circumvents the first-stage regression which can be a bottleneck in modern two-stage procedures for IV regression. We also show that our framework is closely related to the generalized method of moments (GMM) with specific assumptions. This highlights the fundamental connection between GMM and two-stage procedures in IV literature. Using the proposed framework, we develop a simple kernel-based algorithm with consistency guarantees. Lastly, we give empirical results illustrating the advantages of our method over the existing two-stage algorithms.
Simulating the spread of infectious diseases in human communities is critical for predicting the ... more Simulating the spread of infectious diseases in human communities is critical for predicting the trajectory of an epidemic and verifying various policies to control the devastating impacts of the outbreak. Many existing simulators are based on compartment models that divide people into a few subsets and simulate the dynamics among those subsets using hypothesized differential equations. However, these models lack the requisite granularity to study the effect of intelligent policies that influence every individual in a particular way. In this work, we introduce a simulator software capable of modeling a population structure and controlling the disease’s propagation at an individualistic level. In order to estimate the confidence of the conclusions drawn from the simulator, we employ a comprehensive probabilistic approach where the entire population is constructed as a hierarchical random variable. This approach makes the inferred conclusions more robust against sampling artifacts and...
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Papers by Arash Mehrjou