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.
Introduces resemblance structure for large scale geometry.
We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We conduct an extensive study of intrinsic scale for several networks, ranging fro…
The analysis of temporal networks has a wide area of applications in a world of technological advances. An important aspect of temporal network analysis is the discovery of community structures. Real data networks are often very large and the communities are observed to have a hierarchical structure referred to as mult…
We study the concept of coarse disjointness and large scale -to- functions. As a byproduct, we obtain an Ostrand-type characterization of asymptotic dimension for coarse structures. It is shown that properties like finite asymptotic dimension, coarse finitism, large scale weak paracompactness, ect. are all invari…
The paper discusses reducing Hamiltonian systems by scaling and standard symmetries, leading to Kirillov Hamiltonian systems.
StrTransformer recovers sources without labels by optimizing latent matrices and enforcing structural constraints.
Uniformity and proximity are two different ways for defining small scale structures on a set. Coarse structures are large scale counterparts of uniform structures. In this paper, motivated by the definition of proximity, we develop the concept of asymptotic resemblance as a relation between subsets of a set to define a…
This work explores variably scaled kernels to improve non-stationary Gaussian processes.
Improved sparse Gaussian processes using structured scaling matrices and Power-EP framework.
Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large …
The paper presents the comparative study of the nature of stock markets in short-term and long-term time scales with and without structural break in the stock data. Structural break point has been identified by applying Zivot and Andrews structural trend break model to break the original time series (TSO) into time ser…
This study examines cores within superclusters, highlighting their transitional nature and dynamical state.
Study counterfactuals in cyclic systems with shifts and scales.
We uncover scaling laws and statistical structure in complex datasets.
New method approximates controllability of large networks from coarse summaries.
Recent advancements in recurrent neural network (RNN) research have demonstrated the superiority of utilizing multiscale structures in learning temporal representations of time series. Currently, most of multiscale RNNs use fixed scales, which do not comply with the nature of dynamical temporal patterns among sequences…
Behaviors of several laboratory animals can be modeled as sequences of stereotyped behaviors, or behavioral motifs. However, identifying such motifs is a challenging problem. Behaviors have a multi-scale structure: the animal can be simultaneously performing a small-scale motif and a large-scale one (e.g. \textit{chewi…
The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore other properties of the model, like the scaling of its PDF as one take larger …
We propose a method to visualize class similarity in large-scale classifiers.
FaStR improves scalability for time-aware RS with varying coefficients.
Residual Prior Diffusion integrates coarse latent priors with diffusion models for better generative tasks.
We develop a new statistical test for comparing variables with varying scales.
Transformer models perform slower than convolutional networks in learning hierarchical language structures.
Framework for multi-scale clustering using phase transitions.
Study how generalization scales with model size and data in quadratic neural networks.
Study reveals neural scaling laws in random graphs and natural language models.
Network embedding represents nodes in a continuous vector space and preserves structure information from the Network. Existing methods usually adopt a "one-size-fits-all" approach when concerning multi-scale structure information, such as first- and second-order proximity of nodes, ignoring the fact that different scal…
The motivation for this paper is to apply Bayesian structure learning using Model Averaging in large-scale networks. Currently, Bayesian model averaging algorithm is applicable to networks with only tens of variables, restrained by its super-exponential complexity. We present a novel framework, called LSBN(Large-Scale …
A new method for efficient causal structure learning at scale.
SEMASIA provides a large dataset of latent representations for model comparison.
NO approximates non-Markovian BSDEs with polynomial scaling in 1/ε.
The paper introduces structured variational families to improve scalability in black-box variational inference.
A new model for defective media using two scales.
Sparse representations using data dictionaries provide an efficient model particularly for signals that do not enjoy alternate analytic sparsifying transformations. However, solving inverse problems with sparsifying dictionaries can be computationally expensive, especially when the dictionary under consideration has a …
The statistical properties of the increments x(t+T) - x(t) of a financial time series depend on the time resolution T on which the increments are considered. A non-parametric approach is used to study the scale dependence of the empirical distribution of the price increments x(t+T) - x(t) of S&P Index futures, for time…
New method for scalable inference in large-scale regression models with complex error structures.
This paper gives examples of explicit arbitrage-free term structure models with Lévy jumps via state price density approach. By generalizing quadratic Gaussian models, it is found that the probability density function of a Lévy process is a "natural" scale for the process to be the state variable of a market.
A key problem in statistics and machine learning is the determination of network structure from data. We consider the case where the structure of the graph to be reconstructed is known to be scale-free. We show that in such cases it is natural to formulate structured sparsity inducing priors using submodular functions,…
We introduce deep scale-spaces (DSS), a generalization of convolutional neural networks, exploiting the scale symmetry structure of conventional image recognition tasks. Put plainly, the class of an image is invariant to the scale at which it is viewed. We construct scale equivariant cross-correlations based on a princ…
New algorithms estimate Jacobian matrices for large-scale machine learning.
Deep Retrieval learns a retrievable structure for efficient large-scale recommendations.
Study large-scale geometry of graph braid groups via cubical structures.
We present Blitzkriging, a new approach to fast inference for Gaussian processes, applicable to regression, optimisation and classification. State-of-the-art (stochastic) inference for Gaussian processes on very large datasets scales cubically in the number of 'inducing inputs', variables introduced to factorise the mo…
In this paper we show similarities between turbulence and financial systems. Motivated by similarities between the two systems, we construct a multiscale model for hierarchical financial structures that exhibits a constant cascade of wealth from large financial entities to small financial entities. According to our mod…
Exploiting low-rank structure of the user-item rating matrix has been the crux of many recommendation engines. However, existing recommendation engines force raters with heterogeneous behavior profiles to map their intrinsic rating scales to a common rating scale (e.g. 1-5). This non-linear transformation of the rating…
New method scales inference for deep discrete models to thousands of states.
The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland and Toft (1996), and was later extended to the spectrally negative Levy model by Hilberink and Rogers (2002) and Kyprianou and Surya (2007). This paper incorporates the scale effects by allowing the values of ba…
The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series, which is defined as the scale in which the uncertainty is minimized, hence the p…