Related papers: The Sparsity Gap: Uncertainty Principles Proportio…
Theoretically as well as experimentally it is investigated how people represent their knowledge in order to make decisions or to share their knowledge with others. Experiment 1 probes into the ways how people 6ather information about the…
In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of…
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…
Bayesian neural networks and deep ensembles represent two modern paradigms of uncertainty quantification in deep learning. Yet these approaches struggle to scale mainly due to memory inefficiency issues, since they require parameter storage…
Uncertainty sampling is a prevalent active learning algorithm that queries sequentially the annotations of data samples which the current prediction model is uncertain about. However, the usage of uncertainty sampling has been largely…
Disentanglement via mechanism sparsity was introduced recently as a principled approach to extract latent factors without supervision when the causal graph relating them in time is sparse, and/or when actions are observed and affect them…
We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear…
We study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology,…
Uncertainty principle has a fundamental role in quantum theory. This principle states that it is not possible to measure two incompatible observers simultaneously. The uncertainty principle is expressed logically in terms of standard…
It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of…
Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an…
The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory, as quantified recently [Nature Phys. 6, 659 (2010)]. We explore the behavior of the…
The incorporation of systematic uncertainties into confidence interval calculations has been addressed recently in a paper by Conrad et al. (Physical Review D 67 (2003) 012002). In their work, systematic uncertainities in detector…
In high-dimensional sparse regression, would increasing the signal-to-noise ratio while fixing the sparsity level always lead to better model selection? For high-dimensional sparse regression problems, surprisingly, in this paper we answer…
This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…
We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
It is shown that quantum-type coherence, leading to indeterminism and interference of probabilities, may in principle exist in the absence of the Planck constant and a Hamiltonian. Such coherence is a combined effect of a symmetry (not…
The co-sparse analysis model for signals assumes that the signal of interest can be multiplied by an analysis dictionary \Omega, leading to a sparse outcome. This model stands as an interesting alternative to the more classical synthesis…
The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the…