David Draper
Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…
In this work, we investigate the universal representation capacity of the Matrix Product States (MPS) from the perspective of boolean functions and continuous functions. We show that MPS can accurately realize arbitrary boolean functions by…
Markov Chain Monte Carlo (MCMC), and Tensor Networks (TN) are two powerful frameworks for numerically investigating many-body systems, each offering distinct advantages. MCMC, with its flexibility and theoretical consistency, is well-suited…
In this discussion note, we respond to the fascinating paper "Martingale Posterior Distributions" by E. Fong, C. Holmes, and S. G. Walker with a couple of comments. On the basis of previous research, a theorem is stated regarding the…
Model calibration, which is concerned with how frequently the model predicts correctly, not only plays a vital part in statistical model design, but also has substantial practical applications, such as optimal decision-making in the real…
In this work, we study the Neural Tangent Kernel (NTK) of Matrix Product States (MPS) and the convergence of its NTK in the infinite bond dimensional limit. We prove that the NTK of MPS asymptotically converges to a constant matrix during…
The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…
The \textit{Central Limit Theorem (CLT)} is at the heart of a great deal of applied problem-solving in statistics and data science, but the theorem is silent on an important implementation issue: \textit{how much data do you need for the…
Gaussian Process is a non-parametric prior which can be understood as a distribution on the function space intuitively. It is known that by introducing appropriate prior to the weights of the neural networks, Gaussian Process can be…
Latent Dirichlet Allocation (LDA) is a topic model widely used in natural language processing and machine learning. Most approaches to training the model rely on iterative algorithms, which makes it difficult to run LDA on big corpora that…
Gibbs sampling is a Markov Chain Monte Carlo (MCMC) method often used in Bayesian learning. MCMC methods can be difficult to deploy on parallel and distributed systems due to their inherently sequential nature. We study asynchronous Gibbs…
There are multiple proposed interpretations of probability theory: one such interpretation is true-false logic under uncertainty. Cox's Theorem is a representation theorem that states, under a certain set of axioms describing the meaning of…
Gibbs sampling is a widely used Markov chain Monte Carlo (MCMC) method for numerically approximating integrals of interest in Bayesian statistics and other mathematical sciences. Many implementations of MCMC methods do not extend easily to…
We wish to contribute to the discussion of "Comparing Consensus Monte Carlo Strategies for Distributed Bayesian Computation" by offering our views on the current best methods for Bayesian computation, both at big-data scale and with smaller…
In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information…
The redshifted 21-cm monopole is expected to be a powerful probe of the epoch of the first stars and galaxies ($10<z<35$). The global 21-cm signal is sensitive to the thermal and ionization state of hydrogen gas and thus provides a tracer…
Randomized controlled trials play an important role in how Internet companies predict the impact of policy decisions and product changes. In these `digital experiments', different units (people, devices, products) respond differently to the…
Causal inference in observational studies is notoriously difficult, due to the fact that the experimenter is not in charge of the treatment assignment mechanism. Many potential con- founding factors (PCFs) exist in such a scenario, and if…
In the context of the expected-posterior prior (EPP) approach to Bayesian variable selection in linear models, we combine ideas from power-prior and unit-information-prior methodologies to simultaneously produce a minimally-informative…