Related papers: More Permutations Do Not Always Increase Power: No…
Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models…
We describe a general strategy for sampling configurations from a given distribution, NOT based on the standard Metropolis (Markov chain) strategy. It uses the fact that nontrivial problems in statistical physics are high dimensional and…
Consider a central problem in randomized approximation schemes that use a Monte Carlo approach. Given a sequence of independent, identically distributed random variables $X_1,X_2,\ldots$ with mean $\mu$ and standard deviation at most $c…
In recent years, power analysis has become widely used in applied sciences, with the increasing importance of the replicability issue. When distribution-free methods, such as Partial Least Squares (PLS)-based approaches, are considered,…
We investigate in this work the effects of interaction on the fluctuation of empirical measures. The systems with positive definite interaction potentials tend to exhibit smaller fluctuation compared to the fluctuation in standard Monte…
Prior works have shown that in-context learning is brittle to presentation factors such as the order, number, and choice of selected examples. However, ablation-based guidance on selecting the number of examples may ignore the interplay…
Given a distribution in the unite square and having iid sample from it the first question what a statistician might do to test the hypothesis that the sample is iid. For this purpose an extension of the Plancherel measure is introduced.…
Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…
We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
The recently introduced backward Monte-Carlo method [Johan Carlsson, arXiv:math.NA/0010118] is validated, benchmarked, and compared to the conventional, forward Monte-Carlo method by analyzing the error in the Monte-Carlo solutions to a…
We elucidate the origin of large differences (two-fold or more) in the fixed-node errors between the first- vs second-row systems for single-configuration trial wave functions in quantum Monte Carlo calculations. This significant difference…
This paper develops a framework to study the statistical power of revealed-preference tests. With randomly sampled budgets and mild smoothness of demand, statistical learning implies that any model consistent with the data must approximate…
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…
Tossing a coin is the most elementary Monte Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not…
We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expansions for a class of permutation statistics including the…
Inference-time sampling can elicit strong reasoning abilities from language models without additional training. Existing power-sampling methods do so by sharpening the distribution over full generated outputs, favoring completions that are…
The preferential sampling of locations chosen to observe a spatio-temporal process has been identified as a major problem across multiple fields. Predictions of the process can be severely biased when standard statistical methodologies are…
Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…