4 citations · 19 across the 16 of their papers we have counts for
16 papers
The Physical Cutoff Does Not Restore Homogenization: Phase-Dependent Burning in the Strain G-Equation
Michele Caprio
We disprove the expectation stated by Xin, Yu, and Ronney that the physical positive part strain -equation should possess an effective burning velocity in cellular flows. For th…
Distributionally Robust Statistical Verification with Imprecise Neural Networks
Souradeep Dutta, Michele Caprio, Vivian Lin +5
A particularly challenging problem in AI safety is providing guarantees on the behavior of high-dimensional autonomous systems. Verification approaches centered around reachability…
A Novel Bayes' Theorem for Upper Probabilities
Michele Caprio, Yusuf Sale, Eyke Hüllermeier +1
In their seminal 1990 paper, Wasserman and Kadane establish an upper bound for the Bayes' posterior probability of a measurable set , when the prior lies in a class of probabili…
Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?
Yusuf Sale, Michele Caprio, Eyke Hüllermeier
Adequate uncertainty representation and quantification have become imperative in various scientific disciplines, especially in machine learning and artificial intelligence. As an a…
Using Semantic Information for Defining and Detecting OOD Inputs
Ramneet Kaur, Xiayan Ji, Souradeep Dutta +5
As machine learning models continue to achieve impressive performance across different tasks, the importance of effective anomaly detection for such models has increased as well. I…
DC4L: Distribution Shift Recovery via Data-Driven Control for Deep Learning Models
Vivian Lin, Kuk Jin Jang, Souradeep Dutta +3
Deep neural networks have repeatedly been shown to be non-robust to the uncertainties of the real world, even to naturally occurring ones. A vast majority of current approaches hav…
Credal Bayesian Deep Learning
Michele Caprio, Souradeep Dutta, Kuk Jin Jang +4
Uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. Although Bayesian Neural Networks (BNNs) allow…
Constriction for sets of probabilities
Michele Caprio, Teddy Seidenfeld
Given a set of probability measures representing an agent's knowledge on the elements of a sigma-algebra , we can compute upper and lower bounds for the…
Concentration inequalities and optimal number of layers for stochastic deep neural networks
Michele Caprio, Sayan Mukherjee
We state concentration inequalities for the output of the hidden layers of a stochastic deep neural network (SDNN), as well as for the output of the whole SDNN. These results allow…
Refined Pinsker's and reverse Pinsker's inequalities for probability distributions of different dimensions
Michele Caprio
We provide optimal lower and upper bounds for the augmented Kullback-Leibler divergence in terms of the augmented total variation distance between two probability measures defined…
Extended probabilities and their application to statistical inference
Michele Caprio, Sayan Mukherjee
We propose a new, more general definition of extended probability measures. We study their properties and provide a behavioral interpretation. We put them to use in an inference pr…
Dynamic Precise and Imprecise Probability Kinematics
Michele Caprio, Ruobin Gong
We introduce dynamic probability kinematics (DPK), a method for an agent to mechanically update subjective beliefs in the presence of partial information. We then generalize DPK to…
Concerning three classes of non-Diophantine arithmetics
Michele Caprio, Andrea Aveni, Sayan Mukherjee
We present three classes of abstract prearithmetics, , , and . The first one is weakly proj…
Turnpike in infinite dimension
Paolo Leonetti, Michele Caprio
Let be a correspondence from a normed vector space into itself, let be a function, and be an ideal on . Also, assume that the…
Ergodic Theorems for Dynamic Imprecise Probability Kinematics
Michele Caprio, Sayan Mukherjee
We formulate an ergodic theory for the (almost sure) limit of a sequence of successive dynam…
Finite Admixture Models: a Bridge with Stochastic Geometry and Choquet Theory
Michele Caprio, Sayan Mukherjee
Given a finite admixture model whose components and weights are unknown, let the number of identifiable components be a function of the amount of data sampled from a known distribu…