Related papers: New Limits for Knowledge Compilation and Applicati…
We present locally complete inference rules for probabilistic deduction from taxonomic and probabilistic knowledge-bases over conjunctive events. Crucially, in contrast to similar inference rules in the literature, our inference rules are…
Semidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These…
The challenge of creating domain-centric embeddings arises from the abundance of unstructured data and the scarcity of domain-specific structured data. Conventional embedding techniques often rely on either modality, limiting their…
We consider the problem of evaluating representations of data for use in solving a downstream task. We propose to measure the quality of a representation by the complexity of learning a predictor on top of the representation that achieves…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…
Knowledge bases (KBs) are not static entities: new information constantly appears and some of the previous knowledge becomes obsolete. In order to reflect this evolution of knowledge, KBs should be expanded with the new knowledge and…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
In this paper, we develop an exact method for the determination of the minimum sample size for estimating the proportion of a finite population with prescribed margin of error and confidence level. By characterizing the behavior of the…
Top-performing machine learning systems, such as deep neural networks, large ensembles and complex probabilistic graphical models, can be expensive to store, slow to evaluate and hard to integrate into larger systems. Ideally, we would like…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
Multi-distribution learning (MDL), which seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions, has emerged as a unified framework in response to the evolving demand for robustness,…
We study the use of hypermodels to represent epistemic uncertainty and guide exploration. This generalizes and extends the use of ensembles to approximate Thompson sampling. The computational cost of training an ensemble grows with its…
We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…
Integrating domain knowledge into neural networks is a central challenge in scientific machine learning. Three paradigms have emerged -- data-driven (Neural Ordinary Differential Equations, NODEs), soft-constrained (Physics-Informed Neural…
Network reliability is an important metric to evaluate the connectivity among given vertices in uncertain graphs. Since the network reliability problem is known as #P-complete, existing studies have used approximation techniques. In this…
In recent years, deep dictionary learning (DDL)has attracted a great amount of attention due to its effectiveness for representation learning and visual recognition.~However, most existing methods focus on unsupervised deep dictionary…
Deep neural networks have achieved increasingly accurate results on a wide variety of complex tasks. However, much of this improvement is due to the growing use and availability of computational resources (e.g use of GPUs, more layers, more…
On the forefront of scientific computing, Deep Learning (DL), i.e., machine learning with Deep Neural Networks (DNNs), has emerged a powerful new tool for solving Partial Differential Equations (PDEs). It has been observed that DNNs are…
We consider a set of probabilistic functions of some input variables as a representation of the inputs. We present bounds on how informative a representation is about input data. We extend these bounds to hierarchical representations so…