Related papers: Remarks on "Random Sequences"
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for…
Surprisal theory has provided a unifying framework for understanding many phenomena in sentence processing (Hale, 2001; Levy, 2008a), positing that a word's conditional probability given all prior context fully determines processing…
We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered…
We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization…
We propose an alternate approach to quantifying how well language models learn natural language: we ask how well they match the statistical tendencies of natural language. To answer this question, we analyze whether text generated from…
The explanations of large language models have recently been shown to be sensitive to the randomness used for their training, creating a need to characterize this sensitivity. In this paper, we propose a characterization that questions the…
In this paper, we develop a simple approach for testing multiple statistical hypotheses based on the observations of a number of probability ratios enumerated consecutively with respect to the index of hypotheses. Explicit and tight bounds…
We introduce recurrent neural network grammars, probabilistic models of sentences with explicit phrase structure. We explain efficient inference procedures that allow application to both parsing and language modeling. Experiments show that…
In classical statistical decision theory, comparison of experiments plays very important role. Especially, so-called randomization criteria is most important. In this paper, we establish two kinds of quantum analogue these concepts, and…
The distribution function of a random distance in three dimensions is given and some new three-dimensional d2-tests of randomness are suggested. We show that our test statistics are not correlated with the usual test statistics and are…
We study density of rational languages under shift invariant probability measures on spaces of two-sided infinite words, which generalizes the classical notion of density studied in formal languages and automata theory. The density for a…
We survey the classical results on the prime number theorem
We demonstrate that the concerns expressed by Garcia et al. are misplaced, due to (1) a misreading of our findings in [1]; (2) a widespread failure to examine and present words in support of asserted summary quantities based on word usage…
We study the statistical properties of random numbers under the Martin-L\"of definition of randomness, proving that random numbers obey analogues of Strong Law of Large Numbers, the Law of the Iterated Logarithm, and that they are normal.…
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure $\lambda $, a choice needs to be made. One approach is to allow randomness tests to access the measure $\lambda $ as an…
In machine translation (MT) that involves translating between two languages with significant differences in word order, determining the correct word order of translated words is a major challenge. The dependency parse tree of a source…
We present a complete reasoning principle for contextual equivalence in an untyped probabilistic language. The language includes continuous (real-valued) random variables, conditionals, and scoring. It also includes recursion, since the…
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random…
Chinese input recommendation plays an important role in alleviating human cost in typing Chinese words, especially in the scenario of mobile applications. The fundamental problem is to predict the conditional probability of the next word…