Related papers: Solving Probability and Statistics Problems by Pro…

We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…

Programming-by-example is the task of synthesizing a program that is consistent with a set of user-provided input-output examples. As examples are often an under-specification of one's intent, a good synthesizer must choose the intended…

We explore and formalize the task of synthesizing programs over noisy data, i.e., data that may contain corrupted input-output examples. By formalizing the concept of a Noise Source, an Input Source, and a prior distribution over programs,…

This report outlines an approach to learning generative models from data. We express models as probabilistic programs, which allows us to capture abstract patterns within the examples. By choosing our language for programs to be an…

Parameter learning is a crucial task in the field of Statistical Relational Artificial Intelligence: given a probabilistic logic program and a set of observations in the form of interpretations, the goal is to learn the probabilities of the…

We present an algorithm for synthesizing program loops satisfying a given polynomial loop invariant. The class of loops we consider can be modeled by a system of algebraic recurrence equations with constant coefficients. We turn the task of…

This paper investigates the use of different transformations for improving the randomness of sequences. In particular, convolutional codes are used for increasing the size of a given sequence and then a random mapping function is used for…

Large language models, such as OpenAI's codex and Deepmind's AlphaCode, can generate code to solve a variety of problems expressed in natural language. This technology has already been commercialised in at least one widely-used programming…

The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…

This paper considers program synthesis in the context of computational hardness, asking the question: How hard is it to determine whether a given synthesis problem has a solution or not? To answer this question, this paper studies program…

Large pre-trained code generation models, such as OpenAI Codex, can generate syntax- and function-correct code, making the coding of programmers more productive and our pursuit of artificial general intelligence closer. In this paper, we…

Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a…

Instruction subsets (ISs) are heuristics that can shrink the size of the inductive programming (IP) search space by tens of orders of magnitude. Here, we extend the IS approach by introducing instruction and solution probabilities as…

This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build…

Transformation-based learning has been successfully employed to solve many natural language processing problems. It has many positive features, but one drawback is that it does not provide estimates of class membership probabilities. In…

Open-ended tasks, such as coding problems that are common in computer science education, provide detailed insights into student knowledge. However, training large language models (LLMs) to simulate and predict possible student errors in…

Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often…

Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used…

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…

This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…