Related papers: Verifying the Fisher-Yates Shuffle Algorithm in Da…

In sorting situations where the final destination of each item is known, it is natural to repeatedly choose items and place them where they belong, allowing the intervening items to shift by one to make room. (In fact, a special case of…

Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying…

We characterize the minimum-length sequences of independent lazy simple transpositions whose composition is a uniformly random permutation. For every reduced word of the reverse permutation there is exactly one valid way to assign…

Let $M$ be a smooth ($C^{\infty}$) manifold, $F_1,...,F_n$ be vector fields on $M$ generating the corresponding flows $\Phi_1,...,\Phi_n$, and $\alpha_1,...,\alpha_{n}:M\to \mathbb{R}$ smooth functions. Define the following map $f:M\to M$…

Loop invariants play a central role in the verification of imperative programs. However, finding these invariants is often a difficult and time-consuming task for the programmer. We have previously shown how program transformation can be…

Data augmentation in feature space is effective to increase data diversity. Previous methods assume that different classes have the same covariance in their feature distributions. Thus, feature transform between different classes is…

Machine learning systems deployed in the real world must operate under dynamic and often unpredictable distribution shifts. This challenges the validity of statistical safety assurances on the system's risk established beforehand. Common…

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods…

Theorems relating permutations with objects in other fields of mathematics are often stated in terms of avoided patterns. Examples include various classes of Schubert varieties from algebraic geometry (Billey and Abe 2013), commuting…

The approximation of a general $d$-variate function $f$ by the shifts $\phi(\cdot-\xi)$, $\xi\in\Xi\subset \Rd$, of a fixed function $\phi$ occurs in many applications such as data fitting, neural networks, and learning theory. When…

The literal and the initial literal shuffle have been introduced to model the behavior of two synchronized processes. However, it is not possible to describe the synchronization of multiple processes. Furthermore, both restricted forms of…

While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set --`inferring the uncertainty of model parameters on the basis of observations' -- has been continually pursued by many statisticians. To…

Parallel dataflow systems are a central part of most analytic pipelines for big data. The iterative nature of many analysis and machine learning algorithms, however, is still a challenge for current systems. While certain types of bulk…

Classification is a central problem for dynamical systems, in particular for families that arise in a wide range of topics, like substitution subshifts. It is important to be able to distinguish whether two such subshifts are isomorphic,…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

We propose a new, flexible approach for dynamically maintaining successful mutation rates in evolutionary algorithms using $k$-bit flip mutations. The algorithm adds successful mutation rates to an archive of promising rates that are…

Efficient pattern matching is fundamental for practical term rewrite engines. By preprocessing the given patterns into a finite deterministic automaton the matching patterns can be decided in a single traversal of the relevant parts of the…

Reliable estimation of feature contributions in machine learning models is essential for trust, transparency and regulatory compliance, especially when models are proprietary or otherwise operate as black boxes. While permutation-based…

Lexicase selection is a semantic-aware parent selection method, which assesses individual test cases in a randomly-shuffled data stream. It has demonstrated success in multiple research areas including genetic programming, genetic…