Related papers: Effective bi-immunity and randomness

Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion -- almost everywhere computable randomness. A binary sequence…

Relativizing computations of Turing machines to an oracle is a central concept in the theory of computation, both in complexity theory and in computability theory(!). Inspired by lowness notions from computability theory, Allender…

This paper investigates stochastic nondeterminism on continuous state spaces by relating nondeterministic kernels and stochastic effectivity functions to each other. Nondeterministic kernels are functions assigning each state a set o…

Effective versions of strong measure zero sets are developed for various levels of complexity and computability. It is shown that the sets can be equivalently defined using a generalization of supermartingales called odds supermartingales,…

We consider a model for an influenza-like disease, in which, between seasons, the virus makes a random genetic drift $\delta$, (reducing immunity by the factor $\delta$) and obtains a new random transmissibility $\tau$ (closely related to…

Reinforcement learning (RL) in large or infinite state spaces is notoriously challenging, both theoretically (where worst-case sample and computational complexities must scale with state space cardinality) and experimentally (where function…

Machine learning (ML) has been widely used in the literature to automate software engineering tasks. However, ML outcomes may be sensitive to randomization in data sampling mechanisms and learning procedures. To understand whether and how…

We investigate the role of continuous reductions and continuous relativisation in the context of higher randomness. We define a higher analogue of Turing reducibility and show that it interacts well with higher randomness, for example with…

We show that positive measure domination implies uniform almost everywhere domination and that this proof translates into a proof in the subsystem WWKL$_0$ (but not in RCA$_0$) of the equivalence of various Lebesgue measure regularity…

The classical tests in the instrumental variable model can behave arbitrarily if the data is contaminated. For instance, one outlying observation can be enough to change the outcome of a test. We develop a framework to construct testing…

We develop a technique to improve the power of any e-value by a simple randomization involving one independent uniform random variable. Using this framework, we show that two procedures for false discovery rate (FDR) control -- the…

Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either…

Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel…

Much of the field of Machine Learning exhibits a prominent set of failure modes, including vulnerability to adversarial examples, poor out-of-distribution (OoD) detection, miscalibration, and willingness to memorize random labelings of…

SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure…

We present a deterministic mathematical model for malaria transmission with waning immunity. The model consists of five non-linear system of differential equations. We used next generation matrix to derive the basic reproduction number…

This is the second manuscript in a two-part series that uses diagnostic testing to understand the connection between prevalence (i.e. number of elements in a class), uncertainty quantification (UQ), and classification theory. Part I…

In this paper we examine learning methods combining the Random Neural Network, a biologically inspired neural network and the Extreme Learning Machine that achieve state of the art classification performance while requiring much shorter…

The adversarial vulnerability of deep neural networks (DNNs) has been actively investigated in the past several years. This paper investigates the scale-variant property of cross-entropy loss, which is the most commonly used loss function…

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…