Jekyll2021-07-30T12:25:14+00:00https://avt.im/feed.xmlAlexander TereninAlexander TereninMatérn Gaussian Processes on Graphs2021-07-14T00:00:00+00:002021-07-14T00:00:00+00:00https://avt.im/talks/2021/07/14/Graph-Matern-GP<p>Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the input space is Euclidean, the choice is much more limited for Gaussian processes whose input space is an undirected graph. In this work, we leverage the stochastic partial differential equation characterization of Matérn Gaussian processes—a widely-used model class in the Euclidean setting—to study their analog for undirected graphs. We show that the resulting Gaussian processes inherit various attractive properties of their Euclidean and Riemannian analogs and provide techniques that allow them to be trained using standard methods, such as inducing points. This enables graph Matérn Gaussian processes to be employed in mini-batch and non-conjugate settings, thereby making them more accessible to practitioners and easier to deploy within larger learning frameworks.</p>Alexander TereninGaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the input space is Euclidean, the choice is much more limited for Gaussian processes whose input space is an undirected graph. In this work, we leverage the stochastic partial differential equation characterization of Matérn Gaussian processes—a widely-used model class in the Euclidean setting—to study their analog for undirected graphs. We show that the resulting Gaussian processes inherit various attractive properties of their Euclidean and Riemannian analogs and provide techniques that allow them to be trained using standard methods, such as inducing points. This enables graph Matérn Gaussian processes to be employed in mini-batch and non-conjugate settings, thereby making them more accessible to practitioners and easier to deploy within larger learning frameworks.Physically Structured Neural Networks for Smooth and Contact Dynamics2021-07-14T00:00:00+00:002021-07-14T00:00:00+00:00https://avt.im/talks/2021/07/14/Physically-Structured-Networks<p>A neural network’s architecture encodes key information and inductive biases that are used to guide its predictions. In this talk, we discuss recent work which leverages the perspective of neural ordinary differential equations to design network architectures that encode the structures of classical mechanics. We examine the cases of both smooth dynamics and non-smooth contact dynamics. The architectures obtained are easy to understand, show excellent performance and data-efficiency on simple benchmark tasks, and are a promising emerging tool for use in robot learning and related areas.</p>Alexander TereninA neural network’s architecture encodes key information and inductive biases that are used to guide its predictions. In this talk, we discuss recent work which leverages the perspective of neural ordinary differential equations to design network architectures that encode the structures of classical mechanics. We examine the cases of both smooth dynamics and non-smooth contact dynamics. The architectures obtained are easy to understand, show excellent performance and data-efficiency on simple benchmark tasks, and are a promising emerging tool for use in robot learning and related areas.Gaussian Processes on Riemannian Manifolds for Robotics2021-06-21T00:00:00+00:002021-06-21T00:00:00+00:00https://avt.im/talks/2021/06/21/Riemannian-Matern-GP<p>Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the widely-used Matérn class of Gaussian processes has recently been generalized to model functions whose domains are Riemannian manifolds, by re-expressing said processes as solutions of stochastic partial differential equations. In this work, we propose techniques for computing the kernels of these processes on compact Riemannian manifolds via spectral theory of the Laplace–Beltrami operator in a fully constructive manner, thereby allowing them to be trained via standard scalable techniques such as inducing point methods. We also extend the generalization from the Matérn to the widely-used squared exponential Gaussian process. By allowing Riemannian Matérn Gaussian processes to be trained using well-understood techniques, our work enables their use in mini-batch, online, and non-conjugate settings, and makes them more accessible to machine learning practitioners.</p>Alexander TereninGaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the widely-used Matérn class of Gaussian processes has recently been generalized to model functions whose domains are Riemannian manifolds, by re-expressing said processes as solutions of stochastic partial differential equations. In this work, we propose techniques for computing the kernels of these processes on compact Riemannian manifolds via spectral theory of the Laplace–Beltrami operator in a fully constructive manner, thereby allowing them to be trained via standard scalable techniques such as inducing point methods. We also extend the generalization from the Matérn to the widely-used squared exponential Gaussian process. By allowing Riemannian Matérn Gaussian processes to be trained using well-understood techniques, our work enables their use in mini-batch, online, and non-conjugate settings, and makes them more accessible to machine learning practitioners.Aligning Time Series on Incomparable Spaces2021-03-21T00:00:00+00:002021-03-21T00:00:00+00:00https://avt.im/talks/2021/03/21/Aligning-Time-Series-Poster<p>Dynamic time warping (DTW) is a useful method for aligning, comparing and combining time series, but it requires them to live in comparable spaces.
In this work, we consider a setting in which time series live on different spaces without a sensible ground metric, causing DTW to become ill-defined.
To alleviate this, we propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces that avoids the comparability requirement by instead considering intra-relational geometry.
We demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces.
We further propose a smoothed version of GDTW as a differentiable loss and assess its properties in a variety of settings, including barycentric averaging, generative modeling and imitation learning.</p>Alexander TereninDynamic time warping (DTW) is a useful method for aligning, comparing and combining time series, but it requires them to live in comparable spaces. In this work, we consider a setting in which time series live on different spaces without a sensible ground metric, causing DTW to become ill-defined. To alleviate this, we propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces that avoids the comparability requirement by instead considering intra-relational geometry. We demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces. We further propose a smoothed version of GDTW as a differentiable loss and assess its properties in a variety of settings, including barycentric averaging, generative modeling and imitation learning.Learning Contact Dynamics using Physically Structured Neural Networks2021-03-21T00:00:00+00:002021-03-21T00:00:00+00:00https://avt.im/talks/2021/03/21/Contacy-Dynamics-Poster<p>Learning physically structured representations of dynamical systems that include contact between different objects is an important problem for learning-based approaches in robotics. Black-box neural networks can learn to approximately represent discontinuous dynamics, but they typically require large quantities of data and often suffer from pathological behaviour when forecasting for longer time horizons. In this work, we use connections between deep neural networks and differential equations to design a family of deep network architectures for representing contact dynamics between objects. We show that these networks can learn discontinuous contact events in a data-efficient manner from noisy observations in settings that are traditionally difficult for black-box approaches and recent physics inspired neural networks. Our results indicate that an idealised form of touch feedback—which is heavily relied upon by biological systems—is a key component of making this learning problem tractable. Together with the inductive biases introduced through the network architectures, our techniques enable accurate learning of contact dynamics from observations.</p>Alexander TereninLearning physically structured representations of dynamical systems that include contact between different objects is an important problem for learning-based approaches in robotics. Black-box neural networks can learn to approximately represent discontinuous dynamics, but they typically require large quantities of data and often suffer from pathological behaviour when forecasting for longer time horizons. In this work, we use connections between deep neural networks and differential equations to design a family of deep network architectures for representing contact dynamics between objects. We show that these networks can learn discontinuous contact events in a data-efficient manner from noisy observations in settings that are traditionally difficult for black-box approaches and recent physics inspired neural networks. Our results indicate that an idealised form of touch feedback—which is heavily relied upon by biological systems—is a key component of making this learning problem tractable. Together with the inductive biases introduced through the network architectures, our techniques enable accurate learning of contact dynamics from observations.Matérn Gaussian Processes on Graphs2021-03-21T00:00:00+00:002021-03-21T00:00:00+00:00https://avt.im/talks/2021/03/21/Graph-Matern-GP-Poster<p>Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the input space is Euclidean, the choice is much more limited for Gaussian processes whose input space is an undirected graph. In this work, we leverage the stochastic partial differential equation characterization of Matérn Gaussian processes—a widely-used model class in the Euclidean setting—to study their analog for undirected graphs. We show that the resulting Gaussian processes inherit various attractive properties of their Euclidean and Riemannian analogs and provide techniques that allow them to be trained using standard methods, such as inducing points. This enables graph Matérn Gaussian processes to be employed in mini-batch and non-conjugate settings, thereby making them more accessible to practitioners and easier to deploy within larger learning frameworks.</p>Alexander TereninGaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the input space is Euclidean, the choice is much more limited for Gaussian processes whose input space is an undirected graph. In this work, we leverage the stochastic partial differential equation characterization of Matérn Gaussian processes—a widely-used model class in the Euclidean setting—to study their analog for undirected graphs. We show that the resulting Gaussian processes inherit various attractive properties of their Euclidean and Riemannian analogs and provide techniques that allow them to be trained using standard methods, such as inducing points. This enables graph Matérn Gaussian processes to be employed in mini-batch and non-conjugate settings, thereby making them more accessible to practitioners and easier to deploy within larger learning frameworks.Matérn Gaussian Processes on Graphs2021-03-21T00:00:00+00:002021-03-21T00:00:00+00:00https://avt.im/talks/2021/03/21/Graph-Matern-GP<p>Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the input space is Euclidean, the choice is much more limited for Gaussian processes whose input space is an undirected graph. In this work, we leverage the stochastic partial differential equation characterization of Matérn Gaussian processes—a widely-used model class in the Euclidean setting—to study their analog for undirected graphs. We show that the resulting Gaussian processes inherit various attractive properties of their Euclidean and Riemannian analogs and provide techniques that allow them to be trained using standard methods, such as inducing points. This enables graph Matérn Gaussian processes to be employed in mini-batch and non-conjugate settings, thereby making them more accessible to practitioners and easier to deploy within larger learning frameworks.</p>Alexander TereninGaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the input space is Euclidean, the choice is much more limited for Gaussian processes whose input space is an undirected graph. In this work, we leverage the stochastic partial differential equation characterization of Matérn Gaussian processes—a widely-used model class in the Euclidean setting—to study their analog for undirected graphs. We show that the resulting Gaussian processes inherit various attractive properties of their Euclidean and Riemannian analogs and provide techniques that allow them to be trained using standard methods, such as inducing points. This enables graph Matérn Gaussian processes to be employed in mini-batch and non-conjugate settings, thereby making them more accessible to practitioners and easier to deploy within larger learning frameworks.A Brief Tutorial on Multi-armed Bandits2021-03-05T00:00:00+00:002021-03-05T00:00:00+00:00https://avt.im/talks/2021/03/05/Bandits-Tutorial<p>Multi-armed bandits are a class of sequential decision problems which include uncertainty. One of their defining characteristics is the presence of explore-exploit tradeoffs, which require one to balance taking advantage of information that is known with trying different options in order to learn more information in order to make optimal decisions. In this tutorial, we introduce the problem setting and basic techniques of analysis. We conclude by discussing how explore-exploit tradeoffs appear in more general settings, and how the ideas presented can aid in understanding of areas like reinforcement learning.</p>Alexander TereninMulti-armed bandits are a class of sequential decision problems which include uncertainty. One of their defining characteristics is the presence of explore-exploit tradeoffs, which require one to balance taking advantage of information that is known with trying different options in order to learn more information in order to make optimal decisions. In this tutorial, we introduce the problem setting and basic techniques of analysis. We conclude by discussing how explore-exploit tradeoffs appear in more general settings, and how the ideas presented can aid in understanding of areas like reinforcement learning.A Brief Tutorial on Multi-armed Bandits2021-03-04T00:00:00+00:002021-03-04T00:00:00+00:00https://avt.im/talks/2021/03/04/Bandits-Tutorial<p>Multi-armed bandits are a class of sequential decision problems which include uncertainty. One of their defining characteristics is the presence of explore-exploit tradeoffs, which require one to balance taking advantage of information that is known with trying different options in order to learn more information in order to make optimal decisions. In this tutorial, we introduce the problem setting and basic techniques of analysis. We conclude by discussing how explore-exploit tradeoffs appear in more general settings, and how the ideas presented can aid in understanding of areas like reinforcement learning.</p>Alexander TereninMulti-armed bandits are a class of sequential decision problems which include uncertainty. One of their defining characteristics is the presence of explore-exploit tradeoffs, which require one to balance taking advantage of information that is known with trying different options in order to learn more information in order to make optimal decisions. In this tutorial, we introduce the problem setting and basic techniques of analysis. We conclude by discussing how explore-exploit tradeoffs appear in more general settings, and how the ideas presented can aid in understanding of areas like reinforcement learning.Pathwise, spectral, and geometric perspectives on Gaussian processes2021-02-05T00:00:00+00:002021-02-05T00:00:00+00:00https://avt.im/talks/2021/02/05/GP-Perspectives<p>Gaussian processes are usually studied via their finite-dimensional marginal distributions, but this is not the only way to think about them. In this talk, I discuss a little-known result relating Gaussian process priors to posteriors in a path-wise rather than distributional manner, and show how it can be leveraged for efficient posterior sampling. I then present a discussion on different ways of specifying Gaussian process priors, focusing on non-Euclidean settings via techniques based on stochastic partial differential equations and their discrete analogs, which are of particular interest for applications in physical sciences and engineering.</p>Alexander TereninGaussian processes are usually studied via their finite-dimensional marginal distributions, but this is not the only way to think about them. In this talk, I discuss a little-known result relating Gaussian process priors to posteriors in a path-wise rather than distributional manner, and show how it can be leveraged for efficient posterior sampling. I then present a discussion on different ways of specifying Gaussian process priors, focusing on non-Euclidean settings via techniques based on stochastic partial differential equations and their discrete analogs, which are of particular interest for applications in physical sciences and engineering.