Related papers: A theory for the sparsity emerged in the Forward F…
We introduce an enumeration-free method based on mathematical programming to precisely characterize various properties such as fairness or sparsity within the set of "good models", known as Rashomon set. This approach is generically…
Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…
We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides…
Ensuring algorithmic fairness remains a significant challenge in machine learning, particularly as models are increasingly applied across diverse domains. While numerous fairness criteria exist, they often lack generalizability across…
The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…
A frequentist definition of sensitivity of a search for new phenomena is discussed, that has several useful properties. It is based on completely standard concepts, is generally applicable, and has a very clear interpretation. It is…
In this contribution, a stochastic theory for a branching process in a neutron population with two energy levels is investigated. In particular, a variance to mean or Feynman-alpha formula is derived in this generalized scenario using the…
We use freeness assumptions of random matrix theory to analyze the dynamical behavior of inference algorithms for probabilistic models with dense coupling matrices in the limit of large systems. For a toy Ising model, we are able to recover…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our…
To get Bayesian neural networks to perform comparably to standard neural networks it is usually necessary to artificially reduce uncertainty using a "tempered" or "cold" posterior. This is extremely concerning: if the prior is accurate,…
Optimization algorithms appear in the core calculations of numerous Artificial Intelligence (AI) and Machine Learning methods, as well as Engineering and Business applications. Following recent works on the theoretical deficiencies of AI, a…
It is well known that direct training of deep neural networks will generally lead to poor results. A major progress in recent years is the invention of various pretraining methods to initialize network parameters and it was shown that such…
Ever since the seminal work of R. A. Fisher and F. Yates, factorial designs have been an important experimental tool to simultaneously estimate the effects of multiple treatment factors. In factorial designs, the number of treatment…
Sparsity has become popular in machine learning, because it can save computational resources, facilitate interpretations, and prevent overfitting. In this paper, we discuss sparsity in the framework of neural networks. In particular, we…
Deep learning is finding its way into the embedded world with applications such as autonomous driving, smart sensors and aug- mented reality. However, the computation of deep neural networks is demanding in energy, compute power and memory.…
Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior.…
Time-varying parameter (TVP) models have the potential to be over-parameterized, particularly when the number of variables in the model is large. Global-local priors are increasingly used to induce shrinkage in such models. But the…
As one of the most powerful tools for examining the association between functional covariates and a response, the functional regression model has been widely adopted in various interdisciplinary studies. Usually, a limited number of…
This paper is devoted to the theoretical study of the efficiency, namely, stability of some greedy algorithms. In the greedy approximation theory researchers are mostly interested in the following two important properties of an algorithm --…