Related papers: Interpretable Gradient Descent for Kalman Gain
We consider Kalman filtering problems when the observations are intermittently erased or lost. It was known that the estimates are mean-square unstable when the erasure probability is larger than a certain critical value, and stable…
The Kalman filter computes the optimal variable-gain using prior knowledge of the initial state and random (process and measurement) noise distributions, which are assumed to be Gaussian with known variance. However, when these…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…
We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman…
Optimal decision-making under partial observability requires reasoning about the uncertainty of the environment's hidden state. However, most reinforcement learning architectures handle partial observability with sequence models that have…
The optimal predictor for a linear dynamical system (with hidden state and Gaussian noise) takes the form of an autoregressive linear filter, namely the Kalman filter. However, a fundamental problem in reinforcement learning and control…
This paper presents a practical and scalable grid-based state estimation method for high-dimensional models with invertible linear dynamics and with highly non-linear measurements, such as the nearly constant velocity model with…
We consider the problem of optimal control for partially observed dynamical systems. Despite its prevalence in practical applications, there are still very few algorithms available, which take uncertainties in the current state estimates…
We introduce $\mathbf{G}$radient Descent with $\mathbf{A}$daptive $\mathbf{M}$omentum $\mathbf{S}$caling ($\mathbf{Grams}$), a novel optimization algorithm that decouples the direction and magnitude of parameter updates in deep learning.…
Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
The feedback particle filter (FPF) is an innovative, control-oriented and resampling-free adaptation of the traditional particle filter (PF). In the FPF, individual particles are regulated via a feedback gain, and the corresponding gain…
We propose a novel adaptive importance sampling algorithm which incorporates Stein variational gradient decent algorithm (SVGD) with importance sampling (IS). Our algorithm leverages the nonparametric transforms in SVGD to iteratively…
A recently developed data-driven Kalman filter requires offline measurement of the process disturbance; a requirement that is often unmet for many practical applications. We propose a solution that parametrizes the Kalman filter exclusively…
This paper describes InfoGAN, an information-theoretic extension to the Generative Adversarial Network that is able to learn disentangled representations in a completely unsupervised manner. InfoGAN is a generative adversarial network that…
This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast…
We conducted a reproducibility study on Integrated Gradients (IG) based methods and the Important Direction Gradient Integration (IDGI) framework. IDGI eliminates the explanation noise in each step of the computation of IG-based methods…
The error exponent in lossy source coding characterizes the asymptotic decay rate of error probability with respect to blocklength. The Marton's error exponent provides the theoretically optimal bound on this rate. However, computation…
We show that running gradient descent with variable learning rate guarantees loss $f(x) \leq 1.1 \cdot f(x^*) + \epsilon$ for the logistic regression objective, where the error $\epsilon$ decays exponentially with the number of iterations…
This work presents a notion of strong detectability for linear time varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a…