Related papers: Consistency Analysis for the Doubly Stochastic Dir…
The identification of the dependent components in multiple data sets is a fundamental problem in many practical applications. The challenge in these applications is that often the data sets are high-dimensional with few observations or…
This work analyzes the asymptotic performances of fully distributed sequential hypothesis testing procedures as the type-I and type-II error rates approach zero, in the context of a sensor network without a fusion center. In particular, the…
We consider a unique continuation problem where the Dirichlet trace of the solution is known to have finite dimension. We prove Lipschitz stability of the unique continuation problem and design a finite element method that exploits the…
Forecast combination integrates information from various sources by consolidating multiple forecast results from the target time series. Instead of the need to select a single optimal forecasting model, this paper introduces a deep learning…
For a family of stochastic differential equations, we investigate the asymptotic behaviors of its corresponding Picard's iteration, establishing convergence results in terms of relative entropy. Our convergence results complement the…
Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…
We present three tiers of Bayesian consistency tests for the general case of $correlated$ datasets. Building on duplicates of the model parameters assigned to each dataset, these tests range from Bayesian evidence ratios as a global summary…
In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…
Despite the notable success of deep neural networks (DNNs) in solving complex tasks, the training process still remains considerable challenges. A primary obstacle is the substantial time required for training, particularly as high…
Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…
We revisit Wald's celebrated Sequential Probability Ratio Test for sequential tests of two simple hypotheses, under privacy constraints. We propose DP-SPRT, a wrapper that can be calibrated to achieve desired error probabilities and privacy…
Prior work on differential privacy analysis of randomized SGD algorithms relies on composition theorems, where the implicit (unrealistic) assumption is that the internal state of the iterative algorithm is revealed to the adversary. As a…
In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
This article conducts a large dimensional study of a simple yet quite versatile classification model, encompassing at once multi-task and semi-supervised learning, and taking into account uncertain labeling. Using tools from random matrix…
Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of…
Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important. While there are…
Parallel Continual Learning (PCL) tasks investigate the training methods for continual learning with multi-source input, where data from different tasks are learned as they arrive. PCL offers high training efficiency and is well-suited for…
Ensuring that safety-critical applications behave as intended is an important yet challenging task. Modeling languages like differential dynamic logic (dL) have proof calculi capable of proving guarantees for such applications. However, dL…