A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Rule-based classifiers quantify uncertainty using Bernoulli random variables.
problem Quantifying the uncertainty of precision estimates for rule-based text classifiers.
method Treat partitions of sub-strings as Bernoulli random variables, compare means using statistical tests, and combine classifiers using Dempster-Shafer theory.
result The approach can be used to combine binary classifiers into a multi-label classifier.
In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties regarding independence of the nodes are demonstrated. Importantly the model can e…
We consider N Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the proportion LN of variables in a given state converge at rate 1/N as N→∞. Based on these results, we …
We introduce an infectious default and recovery model for N obligors. Obligors are assumed to be exchangeable and their states are described by N Bernoulli random variables S_{i} (i=1,...,N). They are expressed by multiplying independent Bernoulli variables X_{i},Y_{ij},Y'_{ij}, and default and recovery infections are …
The structure of a Bayesian network encodes most of the information about the probability distribution of the data, which is uniquely identified given some general distributional assumptions. Therefore it's important to study the variability of its network structure, which can be used to compare the performance of diff…
We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by expectations of the same functions of independent Bernoulli random variables. This …
The structure of a Bayesian network includes a great deal of information about the probability distribution of the data, which is uniquely identified given some general distributional assumptions. Therefore it's important to study its variability, which can be used to compare the performance of different learning algor…
Dropout improves matrix factorization by acting as a low-rank regularizer.
problem Improving matrix factorization performance through regularization.
method Using Bernoulli random variables to drop columns of factors, demonstrating equivalence to a deterministic model with sum of squared Euclidean norms.
result Dropout achieves the global minimum of a convex approximation problem with squared nuclear norm regularization.
We show how to analyze and interpret the correlation structures, the conditional expectation values and correlation coefficients of exchangeable Bernoulli random variables. We study implied default distributions for the iTraxx-CJ tranches and some popular probabilistic models, including the Gaussian copula model, Beta …
Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficie…
Adaptive learning method identifies and corrects corrupted data.
problem Robust learning from corrupted training sets.
method Identifies corrupted and non-corrupted samples with latent Bernoulli variables, formulates as likelihood maximization with marginalized latent variables, solved via variational inference and Expectation-Maximization.
result Improves over state-of-the-art by automatically inferring corruption level with minimal overhead.
We study in detail and explicitly solve the version of Kyle's model introduced in a specific case in \cite{BB}, where the trading horizon is given by an exponentially distributed random time. The first part of the paper is devoted to the analysis of time-homogeneous equilibria using tools from the theory of one-dimensi…
We present a new explicit formula for the m-th Bernoulli number Bm, which involves two integer parameters a and n with 0≤a≤m≤n. If we set a=0 and n=m, then the formula reduces to the celebrated Kronecker formula for Bm. We give two proofs of our formula. One is analytic and uses a certain fun…
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For d covariates, there are 2d basis coefficients to estimate, which renders conventional approaches computationally prohibitive …
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binary-valued features. Recent work has …