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.
Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods including Tucker and PARAFAC decomposition, (partly) due to their capability of modeling nonlinear rel…
Framework for systemic risk modeling using jointly exchangeable arrays.
This paper characterizes projective models in statistical relational learning.
The study examines convergence of stochastic processes on large graphs and adjacency matrices.
The paper studies stochastic optimization on matrices and its limits as dimensions grow.
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and many other parametric and nonparametric Bayesian models fall within the remit of …
We prove that under fairly general conditions an iterated exchange move gives infinitely many non-conjugate braids. As a consequence, every knot has infinitely many conjugacy classes of n-braid representations if and only if it has one admitting an exchange move.
We show that if a link has a closed -braid representative admitting non-degenerate exchange move, an exchange move that does not obviously preserve the conjugacy class, has infinitely many non-conjugate closed -braid representatives.
The paper develops concentration inequalities for structured random data, extending beyond independent terms.
This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the condition of separate exchangeability. We provide oracle inequalities with rate of c…
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers via a Poisson point process with mean measure on the power set of . Each $E\in\cate$ has a least monotone cover in $\catf$, the collection of monotone subsets of $\cate$, an…
Concentration of infinitely exchangeable sequences with bounded-difference constants
Stochastic partition models tailor a product space into a number of rectangular regions such that the data within each region exhibit certain types of homogeneity. Due to constraints of partition strategy, existing models may cause unnecessary dissections in sparse regions when fitting data in dense regions. To allevia…
New framework models non-exchangeable networks with latent orders and graphons.
Book explores infinite translation surfaces, challenging traditional geometry.
Bayesian Empirical Bayes extends EB to complex structures using probabilistic symmetry.
Improved DOA estimation with distributed sensors across multiple frequencies.
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraph…
Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous, 1981;Hoover, 1979} applies and informs us that the graph is necessarily either dens…
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability …
Study complex reflections in infinite Coxeter tetrahedron moduli space.
This thesis explores supervised classification methods using Bayesian and exchangeability theories.
The family of translation surfaces constructed by Arnoux and Yoccoz from self-similar interval exchange maps encompasses one example from each genus greater than or equal to . We triangulate these surfaces and deduce general properties they share. The surfaces converge to a surface $(X_\i…
New classifiers converge under large data, simplifying complex models.
Distributions over exchangeable matrices with infinitely many columns, such as the Indian buffet process, are useful in constructing nonparametric latent variable models. However, the distribution implied by such models over the number of features exhibited by each data point may be poorly- suited for many modeling tas…
Agents prefer non-diversification in markets with extreme losses.
We study the Immediate Exchange model, recently introduced by Heinsalu and Patriarca [Eur. Phys. J. B 87: 170 (2014)], who showed by simulations that the wealth distribution in this model converges to a Gamma distribution with shape parameter . Here we justify this conclusion analytically, in the infinite-population…
In [Mas82] and [Vee78] it was proved independently that almost every interval exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem implies that these maps mainly have uniformly distributed orbits. This raises the question under which conditions the orbits yield low-discrepancy sequences. The case o…
Deep neural networks' infinite-width behavior approximated by Gaussian models.
Develop conformal prediction for dyadic regression under complex missingness.
Improves magnetic field mapping using an array of magnetometers with noisy input.
Simpler proof for non-basic sets in 2D.
Paper improves DOA estimation in sparse arrays using Siamese neural networks.
Direction of arrival (DoA) estimation of targets improves with the number of elements employed by a phased array radar antenna. Since larger arrays have high associated cost, area and computational load, there is recent interest in thinning the antenna arrays without loss of far-field DoA accuracy. In this context, a c…
Physical activity levels are an important predictor of cardiovascular health and increasingly being measured by sensors, like accelerometers. Accelerometers produce rich multivariate data that can inform important clinical decisions related to individual patients and public health. The CHAMPION study, a study of youth …
Analog arrays are a promising upcoming hardware technology with the potential to drastically speed up deep learning. Their main advantage is that they compute matrix-vector products in constant time, irrespective of the size of the matrix. However, early convolution layers in ConvNets map very unfavorably onto analog a…
Novel CNN array for sign language recognition using wearable IMUs.
We propose a stochastic map model of economic dynamics. In the last decade, an array of observations in economics has been investigated in the econophysics literature, a major example being the universal features of inequality in terms of income and wealth. Another area of inquiry is the formation of opinion in a socie…
We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be positively correlated to their depth in the hierarchy of cross-correlations. We propose…
Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads to a proportional cost whose instantaneous marginal value depends on the current …
In this paper, we study the randomized distributed coordinate descent algorithm with quantized updates. In the literature, the iteration complexity of the randomized distributed coordinate descent algorithm has been characterized under the assumption that machines can exchange updates with an infinite precision. We con…
An infinite parallel tempering bouncy particle sampler improves sampling efficiency for multimodal distributions.
tsbootstrap handles time series uncertainty without assuming independence.
Missing data is an important challenge when dealing with high dimensional data arranged in the form of an array. In this paper, we propose methods for estimation of the parameters of array variate normal probability model from partially observed multiway data. The methods developed here are useful for missing data impu…
New method identifies causal structure in exchangeable data.
Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has been devoted to encoding invariance under symmetry transformations into neural n…
Study collective pricing and hedging with admissible risk exchanges forming a finitely generated convex cone.
Since they were authorized by the U.S. Security and Exchange Commission in 1998, electronic exchanges have boomed, and by 2010 high frequency trading accounted for over 70% of equity trades in the US. Such markets are thought to increase liquidity because of the presence of market makers, who are willing to trade as co…