Related papers: Near-Optimal Estimation of Linear Functionals with…
This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
When attempting to recover functions from observational data, one naturally seeks to do so in an optimal manner with respect to some modeling assumption. With a focus put on the worst-case setting, this is the standard goal of Optimal…
The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…
Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by…
We consider the following signal recovery problem: given a measurement matrix $\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = \Phi\theta^* + \epsilon$ where $\epsilon\in…
Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for…
When is optimal estimation linear? It is well known that, when a Gaussian source is contaminated with Gaussian noise, a linear estimator minimizes the mean square estimation error. This paper analyzes, more generally, the conditions for…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…
The problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise is…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
This work proposes a new loss function targeting classification problems, utilizing a source of information overlooked by cross entropy loss. First, we derive a series of the tightest upper and lower bounds for the probability of a random…
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…
We study the problem of signal estimation from non-linear observations when the signal belongs to a low-dimensional set buried in a high-dimensional space. A rough heuristic often used in practice postulates that non-linear observations may…
This paper proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left…
In the standard Gaussian linear measurement model $Y=X\mu_0+\xi \in \mathbb{R}^m$ with a fixed noise level $\sigma>0$, we consider the problem of estimating the unknown signal $\mu_0$ under a convex constraint $\mu_0 \in K$, where $K$ is a…
We discuss the approach to estimate aggregation and adaptive estimation based upon (nearly optimal) testing of convex hypotheses. We show that in the situation where the observations stem from {\em simple observation schemes} and where set…
The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…