Related papers: Probabilistic Model Counting with Short XORs
Model counting, or counting the satisfying assignments of a Boolean formula, is a fundamental problem with diverse applications. Given #P-hardness of the problem, developing algorithms for approximate counting is an important research area.…
In this paper, we propose a constraint-based modeling approach for the problem of discovering frequent gradual patterns in a numerical dataset. This SAT-based declarative approach offers an additional possibility to benefit from the recent…
We study the query complexity of Weak Parity: the problem of computing the parity of an n-bit input string, where one only has to succeed on a 1/2+eps fraction of input strings, but must do so with high probability on those inputs where one…
Common practice in modern machine learning involves fitting a large number of parameters relative to the number of observations. These overparameterized models can exhibit surprising generalization behavior, e.g., ``double descent'' in the…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…
Relational probabilistic models have the challenge of aggregation, where one variable depends on a population of other variables. Consider the problem of predicting gender from movie ratings; this is challenging because the number of movies…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…
Interpretable Machine Learning faces a recurring challenge of explaining the predictions made by opaque classifiers such as ensemble models, kernel methods, or neural networks in terms that are understandable to humans. When the model is…
Consider the model where we can access a parity function through random uniform labeled examples in the presence of random classification noise. In this paper, we show that approximating the number of relevant variables in the parity…
We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…
The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…
It is almost always easier to find an accurate-but-complex model than an accurate-yet-simple model. Finding optimal, sparse, accurate models of various forms (linear models with integer coefficients, decision sets, rule lists, decision…
The proof of Toda's celebrated theorem that the polynomial hierarchy is contained in $\P^{# P}$ relies on the fact that, under mild technical conditions on the complexity class $C$, we have $\exists C \subset BP \cdot \oplus C$. More…
In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
A new approach to solving random matrix models directly in the large $N$ limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large $N$ loop equations are then used to generate values of…
A sample of n generic points in the xy-plane defines a permutation that relates their ranks along the two axes. Every subset of k points similarly defines a pattern, which occurs in that permutation. The number of occurrences of small…
A standard method for designing randomized algorithms to approximately count the number of solutions of a problem in $\#$P, is by constructing a rapidly mixing Markov chain converging to the uniform distribution over this set of solutions.…
Probably Approximately Correct (PAC) bounds are widely used to derive probabilistic guarantees for the generalisation of machine learning models. They highlight the components of the model which contribute to its generalisation capacity.…