Related papers: Sparsity vs. Statistical Independence in Adaptive …
Permutation tests have been proposed by Albert et al. (2015) to detect dependence between point processes, modeling in particular spike trains, that is the time occurrences of action potentials emitted by neurons. Our present work focuses…
We consider the linearly transformed spiked model, where observations $Y_i$ are noisy linear transforms of unobserved signals of interest $X_i$: \begin{align*} Y_i = A_i X_i + \varepsilon_i, \end{align*} for $i=1,\ldots,n$. The transform…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
Complex systems are typically characterized as an intermediate situation between a complete regular structure and a random system. Brain signals can be studied as a striking example of such systems: cortical states can range from highly…
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…
Sequences of events in noise-driven excitable systems with slow variables often show serial correlations among their intervals of events. Here, we employ a master equation for general non-renewal processes to calculate the interval and…
Spiking Neural Networks (SNNs) offer inherent advantages for low-power inference through sparse, event-driven computation. However, the theoretical energy benefits of SNNs are often decoupled from real hardware performance due to the opaque…
Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix $X \in \mathbb{R}^{N \times d}$ and measurements or labels ${y} \in \mathbb{R}^N$ where ${y} = {X}…
A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d.…
In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction.…
Neuromorphic applications emulate the processing performed by the brain by using spikes as inputs instead of time-varying analog stimuli. Therefore, these time-varying stimuli have to be encoded into spikes, which can induce important…
Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…
Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even system failure is sometimes difficult…
Sequential, multiple assignment randomized trials (SMARTs), which assist in the optimization of adaptive interventions, are growing in popularity in education and behavioral sciences. This is unsurprising, as adaptive interventions reflect…