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There exists a dichotomy between classical probabilistic graphical models, such as Bayesian networks (BNs), and modern tractable models, such as sum-product networks (SPNs). The former generally have intractable inference, but provide a…
The PC algorithm is a widely used method in causal inference for learning the structure of Bayesian networks. Despite its popularity, the PC algorithm suffers from significant time complexity, particularly as the size of the dataset…
Consider a Bayesian inference problem where a variable of interest does not take values in a Euclidean space. These "non-standard" data structures are in reality fairly common. They are frequently used in problems involving latent discrete…
This thesis investigates how the sub-structure of words can be accounted for in probabilistic models of language. Such models play an important role in natural language processing tasks such as translation or speech recognition, but often…
Strong bisimilarity on normed BPA is polynomial-time decidable, while weak bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the computational complexity of branching bisimilarity on totally normed BPA lies. This…
Bayesian networks are a canonical formalism for representing probabilistic dependencies, yet their integration within logic programming frameworks remains a nontrivial challenge, mainly due to the complex structure of these networks. In…
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory -- in the discrete setting of bits and Turing machines. Over real numbers, on the other hand, the…
Proving lower bounds remains the most difficult of tasks in computational complexity theory. In this paper, we show that whereas most natural NP-complete problems belong to NLIN (linear time on nondeterministic RAMs), some of them,…
Best subset selection (BSS) is widely known as the holy grail for high-dimensional variable selection. Nevertheless, the notorious NP-hardness of BSS substantially restricts its practical application and also discourages its theoretical…
Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…
In the BCSS model of real number computations we prove a concrete and explicit semi-decidable language to be undecidable yet not reducible from (and thus strictly easier than) the real Halting Language. This solution to Post's Problem over…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
Program synthesis from natural language (NL) is practical for humans and, once technically feasible, would significantly facilitate software development and revolutionize end-user programming. We present SAPS, an end-to-end neural network…
We study the computational power of machines that specify their own acceptance types, and show that they accept exactly the languages that $\manyonesharp$-reduce to NP sets. A natural variant accepts exactly the languages that…
BSS RAMs were introduced to provide a mathematical framework for characterizing algorithms over first-order structures. Non-deterministic BSS RAMs help to model different non-deterministic approaches. Here, we deal with different types of…
Neural Networks (NNs) have been widely {used in supervised learning} due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability…
We study the class of languages that have membership proofs which can be verified by real-time finite-state machines using only a constant number of random bits, regardless of the size of their inputs. Since any further restriction on the…
In this paper we introduce a continuous time stochastic neurite branching model closely related to the discrete time stochastic BES-model. The discrete time BES-model is underlying current attempts to simulate cortical development, but is…
Low-dimensional probability models for local distribution functions in a Bayesian network include decision trees, decision graphs, and causal independence models. We describe a new probability model for discrete Bayesian networks, which we…
Extraction of latent sources of complex stimuli is critical for making sense of the world. While the brain solves this blind source separation (BSS) problem continuously, its algorithms remain unknown. Previous work on…