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Natural gradients can improve convergence in stochastic variational inference significantly but inverting the Fisher information matrix is daunting in high dimensions. Moreover, in Gaussian variational approximation, natural gradient…
Natural Gradient Descent, a second-degree optimization method motivated by the information geometry, makes use of the Fisher Information Matrix instead of the Hessian which is typically used. However, in many cases, the Fisher Information…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…
Gradient regularization (GR) has been shown to improve the generalizability of trained models. While Natural Gradient Descent has been shown to accelerate optimization in the initial phase of training, little attention has been paid to how…
We introduce a simple algorithm, True Asymptotic Natural Gradient Optimization (TANGO), that converges to a true natural gradient descent in the limit of small learning rates, without explicit Fisher matrix estimation. For quadratic models…
This paper introduces a novel proprioceptive state estimator for legged robots that combines model-based filters and deep neural networks. Recent studies have shown that neural networks such as multi-layer perceptron or recurrent neural…
The graphical Lasso (GLASSO) is a widely used algorithm for learning high-dimensional undirected Gaussian graphical models (GGM). Given i.i.d. observations from a multivariate normal distribution, GLASSO estimates the precision matrix by…
We consider the problem of learning observation models for robot state estimation with incremental non-differentiable optimizers in the loop. Convergence to the correct belief over the robot state is heavily dependent on a proper tuning of…
This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix Lie group with invariance properties. The problem of an invariant continuous-time model with discrete-time measurements is cast into…
The state-space model and the Kalman filter provide us with unified and computationaly efficient procedure for computing the log-likelihood of the diverse type of time series models. This paper presents an algorithm for computing the…
We propose Neural Gradient Learning (NGL), a deep learning approach to learn gradient vectors with consistent orientation from 3D point clouds for normal estimation. It has excellent gradient approximation properties for the underlying…
There is a clear need for efficient algorithms to tune hyperparameters for statistical learning schemes, since the commonly applied search methods (such as grid search with N-fold cross-validation) are inefficient and/or approximate.…
Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and…
High sensitivity of neural architecture search (NAS) methods against their input such as step-size (i.e., learning rate) and search space prevents practitioners from applying them out-of-the-box to their own problems, albeit its purpose is…
In safety-critical scenarios, the protection level of the autonomous navigation system is crucial for enabling mobile robots to perform safe tasks. However, existing studies on probabilistic navigation systems for robots usually perform…
Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…
We propose estimating Gaussian graphical models (GGMs) that are fair with respect to sensitive nodal attributes. Many real-world models exhibit unfair discriminatory behavior due to biases in data. Such discrimination is known to be…
Policy gradient algorithms are widely used in reinforcement learning and belong to the class of approximate dynamic programming methods. This paper studies two key policy gradient algorithms, the Natural Policy Gradient and the Gauss-Newton…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…