相关论文: Evaluation of DNF Formulas

In many applications, it is desirable to extract only the relevant information from complex input data, which involves making a decision about which input features are relevant. The information bottleneck method formalizes this as an…

This work focuses on a specific classification problem, where the information about a sample is not readily available, but has to be acquired for a cost, and there is a per-sample budget. Inspired by real-world use-cases, we analyze average…

High-dimensional Bayesian inverse analysis (dim >> 100) is mostly unfeasible for computationally demanding, nonlinear physics-based high-fidelity (HF) models. Usually, the use of more efficient gradient-based inference schemes is impeded if…

We study the approximation of expectations $\E(f(X))$ for solutions $X$ of SDEs and functionals $f \colon C([0,1],\R^r) \to \R$ by means of restricted Monte Carlo algorithms that may only use random bits instead of random numbers. We…

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

This paper describes a purely functional library for computing level-$p$-complexity of Boolean functions, and applies it to two-level iterated majority. Boolean functions are simply functions from $n$ bits to one bit, and they can describe…

To support real-world decision-making, it is crucial for models to be well-calibrated, i.e., to assign reliable confidence estimates to their predictions. Uncertainty quantification is particularly important in personalized federated…

In this paper, we study the problem of learning a monotone DNF with at most $s$ terms of size (number of variables in each term) at most $r$ ($s$ term $r$-MDNF) from membership queries. This problem is equivalent to the problem of learning…

Conventional federated learning (FL) frameworks often suffer from training degradation due to data uncertainty and heterogeneity across local clients. Probabilistic approaches such as Bayesian neural networks (BNNs) can mitigate this issue…

Since its introduction by Valiant in 1984, PAC learning of DNF expressions remains one of the central problems in learning theory. We consider this problem in the setting where the underlying distribution is uniform, or more generally, a…

Deep Neural Networks (DNN) are core components for classification and regression tasks of many software systems. Companies incur in high costs for testing DNN with datasets representative of the inputs expected in operation, as these need…

Given a CNF formula $F$, we present a new algorithm for deciding the satisfiability (SAT) of $F$ and computing all solutions of assignments. The algorithm is based on the concept of \emph{cofactors} known in the literature. This paper is a…

Causal inference methods are widely applied in various decision-making domains such as precision medicine, optimal policy and economics. Central to causal inference is the treatment effect estimation of intervention strategies, such as…

We introduce a new numerical algorithm for solving the stochastic neural field equation (NFE) with delays. Using this algorithm we have obtained some numerical results which illustrate the effect of noise in the dynamical behaviour of…

Conditional density estimation (CDE) is a fundamental task in machine learning that aims to model the full conditional law $\mathbb{P}(\mathbf{y} \mid \mathbf{x})$, beyond mere point prediction (e.g., mean, mode). A core challenge is…

We consider stochastic optimization under distributional uncertainty, where the unknown distributional parameter is estimated from streaming data that arrive sequentially over time. Moreover, data may depend on the decision of the time when…

Boson sampling is a mathematical problem that is strongly believed to be intractable for classical computers, whereas passive linear interferometers can produce samples efficiently. So far, the problem remains a computational curiosity, and…

This paper tackles the problem of solving stochastic optimization problems with a decision-dependent distribution in the setting of stochastic strongly-monotone games and when the distributional dependence is unknown. A two-stage approach…

In today's era, Neural Networks (NN) are applied in various scientific fields such as robotics, medicine, engineering, etc. However, the predictions of neural networks themselves contain a degree of uncertainty that must always be taken…

This paper provides lower bounds on the convergence rate of Derivative Free Optimization (DFO) with noisy function evaluations, exposing a fundamental and unavoidable gap between the performance of algorithms with access to gradients and…