Related papers: Submodular Functions Are Noise Stable
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force…
Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow \cite{KZ:PAMI04} has had significant impact in computer vision \cite{BVZ:PAMI01,Kwatra:SIGGRAPH03,Rother:GrabCut04}.…
Driven quantum nonlinear oscillators, while essential for quantum technologies, are generally prone to complex chaotic dynamics that fall beyond the reach of perturbative analysis. By focusing on subharmonic bifurcations of a harmonically…
Noiseless subsystems offer a general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. A paradigmatic class of error models displaying non-trivial symmetries emerges under…
In many applications, the common assumption that a driving noise process affecting a system is independent or Markovian may not be realistic, but the noise process may be assumed to be stationary. To study such problems, this paper…
One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth in certain subdomains will have good approximations in…
Designing objective functions robust to label noise is crucial for real-world classification algorithms. In this paper, we investigate the robustness to label noise of an $f$-divergence-based class of objective functions recently proposed…
We show that for any constant $\epsilon > 0$ and $p \ge 1$, it is possible to distinguish functions $f : \{0,1\}^n \to [0,1]$ that are submodular from those that are $\epsilon$-far from every submodular function in $\ell_p$ distance with a…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
Meta-Learning has gained increasing attention in the machine learning and artificial intelligence communities. In this paper, we introduce and study an adaptive submodular meta-learning problem. The input of our problem is a set of items,…
Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions Constrained submodular function…
Fourier embedding has shown great promise in removing spectral bias during neural network training. However, it can still suffer from high generalization errors, especially when the labels or measurements are noisy. We demonstrate that…
Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution,…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
We consider the problem of learning an unknown $f$ with a sparse Fourier spectrum in the presence of outlier noise. In particular, the algorithm has access to a noisy oracle for (an unknown) $f$ such that (i) the Fourier spectrum of $f$ is…
Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…
Stationary (limiting) distributions of shot noise processes, with exponential response functions, form a large subclass of positive selfdecomposable distributions that we illustrate by many examples. These shot noise distributions are…
The noise sensitivity of a Boolean function describes its likelihood to flip under small perturbations of its input. Introduced in the seminal work of Benjamini, Kalai and Schramm [Inst. Hautes \'{E}tudes Sci. Publ. Math. 90 (1999) 5-43],…
Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external…
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…