相关论文: Learning Fricke signs from Maass form Coefficients

In this paper, we relate the framework of mod-$\phi$ convergence to the construction of approximation schemes for lattice-distributed random variables. The point of view taken here is that of Fourier analysis in the Wiener algebra, allowing…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

Motivated by recently emerging problems in machine learning and statistics, we propose data models which relax the familiar i.i.d. assumption. In essence, we seek to understand what it means for data to come from a set of probability…

The adverse drug reactions (ADRs) predicted based on the biased records in FAERS (U.S. Food and Drug Administration Adverse Event Reporting System) may mislead diagnosis online. Generally, such problems are solved by optimizing reporting…

We propose a federated averaging Langevin algorithm (FA-LD) for uncertainty quantification and mean predictions with distributed clients. In particular, we generalize beyond normal posterior distributions and consider a general class of…

There has been an increasing interest from the scientific community in using likelihood-free inference (LFI) to determine which parameters of a given simulator model could best describe a set of experimental data. Despite exciting recent…

Fisher Discriminant Analysis (FDA) is one of the essential tools for feature extraction and classification. In addition, it motivates the development of many improved techniques based on the FDA to adapt to different problems or data types.…

Face recognition (FR) systems have a growing effect on critical decision-making processes. Recent works have shown that FR solutions show strong performance differences based on the user's demographics. However, to enable a trustworthy FR…

We introduce the notion of classical fractional query algorithms, which generalize decision trees in the average-case setting, and can potentially perform better than them. We show that the limiting run-time complexity of a natural class of…

Data assimilation (DA) is crucial for enhancing solutions to partial differential equations (PDEs), such as those in numerical weather prediction, by optimizing initial conditions using observational data. Variational DA methods are widely…

Andrews recently introduced k-marked Durfee symbols, which are a generalization of partitions that are connected to moments of Dyson's rank statistic. He used these connections to find identities relating their generating functions as well…

As they have a vital effect on social decision-making, AI algorithms should be not only accurate but also fair. Among various algorithms for fairness AI, learning fair representation (LFR), whose goal is to find a fair representation with…

In the literature, finite mixture models are described as linear combinations of probability distribution functions having the form $\displaystyle f(x) = \Lambda \sum_{i=1}^n w_i f_i(x)$, $x \in \mathbb{R}$, where $w_i$ are positive…

We revisit Deep Linear Discriminant Analysis (Deep LDA) from a likelihood-based perspective. While classical LDA is a simple Gaussian model with linear decision boundaries, attaching an LDA head to a neural encoder raises the question of…

In many data classification problems, there is no linear relationship between an explanatory and the dependent variables. Instead, there may be ranges of the input variable for which the observed outcome is signficantly more or less likely.…

\textit{Mallows model} is a widely-used probabilistic framework for learning from ranking data, with applications ranging from recommendation systems and voting to aligning language models with human preferences~\cite{chen2024mallows,…

In this paper we show that the classical problem of frequency estimation can be formulated and solved efficiently in an empirical Bayesian framework by assigning a uniform a priori probability distribution to the unknown frequency. We…

Machine learning (ML) is increasingly becoming a helpful tool in the search for novel functional compounds. Here we use classification via random forests to predict the stability of half-Heusler (HH) compounds, using only experimentally…

Algorithms in machine learning and AI do critically depend on at least three key components: (i) the risk function, which is the expectation of the loss function, (ii) the function space, which is often called the hypothesis space, and…

Ensemble forecast based on physics-informed models is one of the most widely used forecast algorithms for complex turbulent systems. A major difficulty in such a method is the model error that is ubiquitous in practice. Data-driven machine…