Related papers: Rank-one Multi-Reference Factor Analysis
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…
In this paper, we establish sample complexity bounds for learning high-dimensional simplices in $\mathbb{R}^K$ from noisy data. Specifically, we consider $n$ i.i.d. samples uniformly drawn from an unknown simplex in $\mathbb{R}^K$, each…
We show that the gradient estimates used in training Deep Gaussian Processes (DGPs) with importance-weighted variational inference are susceptible to signal-to-noise ratio (SNR) issues. Specifically, we show both theoretically and via an…
kNN is a very effective Instance based learning method, and it is easy to implement. Due to heterogeneous nature of data, noises from different possible sources are also widespread in nature especially in case of large-scale databases. For…
We use an artificial neural network to analyze asymmetric noisy random telegraph signals (RTSs), and extract underlying transition rates. We demonstrate that a long short-term memory neural network can vastly outperform conventional…
The signal-to-noise ratio (SNR) is a fundamental tool to measure the performance of an image sensor. However, confusions sometimes arise between the two types of SNRs. The first one is the output-referred SNR which measures the ratio…
Analysing data that consists of one or more truncated exponential functions is of great interest in a wide range of fields. Data consisting of one or more exponential functions are measured by a wide range of instruments, examples include:…
Policy-gradient methods are widely used in reinforcement learning, yet training often becomes unstable or slows down as learning progresses. We study this phenomenon through the noise-to-signal ratio (NSR) of a policy-gradient estimator,…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
We study estimation and clustering in Gaussian mixture models under variance misspecification. Observations are generated with true variance $\sigma^2$, while the component means are estimated using a likelihood with variance $\tau^2$,…
A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of…
The interdependence and high dimensionality of multivariate signals present significant challenges for denoising, as conventional univariate methods often struggle to capture the complex interactions between variables. A successful approach…
Searching for gravitational-wave signals is a challenging and computationally intensive endeavor undertaken by multiple independent analysis pipelines. While detection depends only on observed noisy data, it is sometimes inconsistently…
An observed $K$-dimensional series $\left\{ y_{n}\right\} _{n=1}^{N}$ is expressed in terms of a lower $p$-dimensional latent series called factors $f_{n}$ and random noise $\varepsilon_{n}$. The equation, $y_{n}=Qf_{n}+\varepsilon_{n}$ is…
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
The scale of functional magnetic resonance image data is rapidly increasing as large multi-subject datasets are becoming widely available and high-resolution scanners are adopted. The inherent low-dimensionality of the information in this…
In this paper, a sparse-based method for the estimation of the parameters of multidimensional ($R$-D) modal (harmonic or damped) complex signals in noise is presented. The problem is formulated as $R$ simultaneous sparse approximations of…
Distant and weak supervision allow to obtain large amounts of labeled training data quickly and cheaply, but these automatic annotations tend to contain a high amount of errors. A popular technique to overcome the negative effects of these…
Neural networks (NNs) are making a large impact both on research and industry. Nevertheless, as NNs' accuracy increases, it is followed by an expansion in their size, required number of compute operations and energy consumption. Increase in…