Related papers: Experimenting with Standard Young Tableaux
We introduce Joint Probability Trees (JPT), a novel approach that makes learning of and reasoning about joint probability distributions tractable for practical applications. JPTs support both symbolic and subsymbolic variables in a single…
Examples of small contingency tables on binary random variables with large integer programming gaps on the lower bounds of cell entries were constructed by Sullivant. We argue here that the margins for which these constructed large gaps…
The confusion matrix, a ubiquitous visualization for helping people evaluate machine learning models, is a tabular layout that compares predicted class labels against actual class labels over all data instances. We conduct formative…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
Causal discovery amounts to unearthing causal relationships amongst features in data. It is a crucial companion to causal inference, necessary to build scientific knowledge without resorting to expensive or impossible randomised control…
Signal Processing (SP) and Machine Learning (ML) rely on good math and coding knowledge, in particular, linear algebra, probability, trigonometry, and complex numbers. A good grasp of these relies on scalar algebra learned in middle school.…
Tables store rich numerical data, but numerical reasoning over tables is still a challenge. In this paper, we find that the spreadsheet formula, which performs calculations on numerical values in tables, is naturally a strong supervision of…
Spreadsheet tables are often labeled, and these labels effectively constitute types for the data in the table. In such cases tables can be considered to be built from typed data where the placement of values within the table is controlled…
Scientific software is, by its very nature, complex. It is mathematical and highly optimized which makes it prone to subtle bugs not as easily detected by traditional testing. We outline how symbolic execution can be used to write tests…
The Selberg integral is an important integral first evaluated by Selberg in 1944. Stanley found a combinatorial interpretation of the Selberg integral in terms of permutations. In this paper, new combinatorial objects "Young books" are…
The understanding of probability can be difficult for a few young scientists. Consequently, this new mathematical symbol, related to binomial coefficients and simplicial polytopic numbers, could be helpful to science education. Moreover,…
We investigate finite right-distributive binary algebraic structures called shelves. We first use symbolic computations with Python to classify (up to isomorphism) all connected shelves with order less than six. We explore the group…
The technique of guessing can be very fruitful when dealing with sequences which arise in practice. This holds true especially when guessing is performed algorithmically and efficiently. One highly useful tool for this purpose is the…
We propose a new class of probabilistic neural-symbolic models, that have symbolic functional programs as a latent, stochastic variable. Instantiated in the context of visual question answering, our probabilistic formulation offers two key…
Cellular signaling is essential in information processing and decision making. Therefore, a variety of experimental approaches have been developed to study signaling on bulk and single-cell level. Single-cell measurements of signaling…
We construct examples of contingency tables on $n$ binary random variables where the gap between the linear programming lower/upper bound and the true integer lower/upper bounds on cell entries is exponentially large. These examples provide…
We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced $\textit{probabilistic divide-and-conquer}$ technique. A simple exact sampling algorithm is presented for…
Let $G$ be a commutative algebraic group embedded in projective space and $\Gamma$ a finitely generated subgroup of $G$. From these data we construct a chain of algebraic subgroups of $G$ which is intimately related to obstructions to…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. Several classical probabilistic inference tasks (such as MAP and computing marginals) have not yet received a lot of attention for…
We study the class of functions on the set of (generalized) Young diagrams arising as the number of embeddings of bipartite graphs. We give a criterion for checking when such a function is a polynomial function on Young diagrams (in the…