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.
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach requires looking for a good representation that reveals the signal structure, and sol…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample to be dependent on the sample size, a feature not presented in a …
We study the Bayesian model averaging approach to learning Bayesian network structures (DAGs) from data. We develop new algorithms including the first algorithm that is able to efficiently sample DAGs according to the exact structure posterior. The DAG samples can then be used to construct estimators for the posterior …
Bayesian Networks (BNs) are useful tools giving a natural and compact representation of joint probability distributions. In many applications one needs to learn a Bayesian Network (BN) from data. In this context, it is important to understand the number of samples needed in order to guarantee a successful learning. Pre…
The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both structurally consistent and risk consistent and the error probability of structure …
We apply our statistically deterministic machine learning/clustering algorithm *K-means (recently developed in https://ssrn.com/abstract=2908286) to 10,656 published exome samples for 32 cancer types. A majority of cancer types exhibit mutation clustering structure. Our results are in-sample stable. They are also out-o…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolutionary trees. The …
The paper proposes a method to learn the structure of continuous-action games with non-parametric utilities using a limited number of samples.
problem Learning the exact structure of continuous-action games with non-parametric utility functions.
method An ℓ1 regularized method that encourages sparsity of the Fourier transform coefficients of the utility functions, accessed via a few Nash equilibria and their noisy utilities.
result The method recovers the exact structure of the utility functions and the game structure with provable theoretical guarantees.
We present a novel condition, which we term the net- work nullspace property, which ensures accurate recovery of graph signals representing massive network-structured datasets from few signal values. The network nullspace property couples the cluster structure of the underlying network-structure with the geometry of th…
This paper presents an out-of-sample prediction comparison between major machine learning models and the structural econometric model. Over the past decade, machine learning has established itself as a powerful tool in many prediction applications, but this approach is still not widely adopted in empirical economic stu…
We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled partial order, the conditional probabilities of interest are computed exactly. We…
BDeu marginal likelihood score is a popular model selection criterion for selecting a Bayesian network structure based on sample data. This non-informative scoring criterion assigns same score for network structures that encode same independence statements. However, before applying the BDeu score, one must determine a …
Random column sampling is not guaranteed to yield data sketches that preserve the underlying structures of the data and may not sample sufficiently from less-populated data clusters. Also, adaptive sampling can often provide accurate low rank approximations, yet may fall short of producing descriptive data sketches, es…
The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse Bayesian learning model from our previous work, we propose two Gibbs sampling algori…
Recently introduced generative adversarial network (GAN) has been shown numerous promising results to generate realistic samples. The essential task of GAN is to control the features of samples generated from a random distribution. While the current GAN structures, such as conditional GAN, successfully generate samples…
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization problem. Almost all previous work assumes no explicit structure of the matrix and uses…