In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool to measure and control the market risk of an asset or a portfolio, and it is also required for regulatory purposes. Its popularity is partly due to the fact …
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48 results for “product partition model”
The study examines the balancedness of random partition models and finds the rich-get-richer characteristic is a result of model assumptions.
problem The balancedness of random partition models is largely neglected in the literature.
method Formulated a framework to define and study the balancedness of exchangeable random partition models, analyzed using product-form exchangeability and projectivity assumptions.
result The 'rich-get-richer' characteristic is an inevitable consequence of the model assumptions.
Dynamic Partition Modelsstat.ML
Dynamic partition models learn compact binary representations from data.
problem Learning accurate distributed representations of high-dimensional data.
method The approach involves partitioning variables into expert supports, dynamically adapting partitions based on active experts, and using a smoothed version of the model with separate mixtures for each data dimension.
result Accurate reconstructions of high-dimensional data points achieved with a dozen experts.
Norm-range partition improves MIPS search efficiency by reducing query complexity.
problem Efficiently searching for maximum inner product in large datasets.
method Norm-range partition technique that divides datasets into sub-datasets with similar norms and builds independent hash indexes.
result Significantly reduces the number of probed buckets for LSH-based MIPS algorithms.
The key limiting factor in graphical model inference and learning is the complexity of the partition function. We thus ask the question: what are general conditions under which the partition function is tractable? The answer leads to a new kind of deep architecture, which we call sum-product networks (SPNs). SPNs are d…
SPP improves partitioning of sparse regions in multi-dimensional arrays.
problem Existing partition models cause unnecessary dissections in sparse regions.
method SPP uses an 'enclosing' strategy to attach patches to dense regions, making it self-consistent for infinite arrays.
result SPP outperforms state-of-the-arts in relational modeling.
Detecting Free Products in the Mapping Class Group of Punctured Disks via Dynnikov Coordinatesmath.GT
Algorithm detects free products in disk mapping class groups.
problem Detecting free products in mapping class groups of punctured disks.
method Algorithm based on Dynnikov coordinates to verify completeness and reveal free product structure.
result Algorithm determines exact structure of free products generated by Dehn twists.
Markov partitions for the geodesic flow on compact Riemann surfaces of constant negative curvaturemath.DG
The paper constructs Markov partitions for geodesic flow on hyperbolic surfaces.
problem Understanding Markov partitions for general hyperbolic flows.
method Rigorous construction of Markov partitions for geodesic flow on Riemann surfaces of constant negative curvature.
result Explicit forms of rectangles and local cross sections provided for the geodesic flow.
Researchers compute dimensions of GLN-skein modules for genus-one mapping tori.
problem Computing dimensions of GLN-skein modules for mapping tori.
method Explicit Euler product expansion of the skein partition function.
result Explicit computation of dimensions and generating function.
Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a certain coarse transversality condition. Let E be a Hermitean bundle with connection on M. We define a coarse multi-partitioned index of the…
In this paper, we consider the problem of partitioning a small data sample drawn from a mixture of product distributions. We are interested in the case that individual features are of low average quality , and we want to use as few of them as possible to correctly partition the sample. We analyze a spectral tech…
We study 4-dimensional higher-derivative conformal higher spin (CHS) fields generalising Weyl graviton and conformal gravitino. They appear, in particular, as "induced" theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. …
Differentially private method for synthetic data generation from vertically partitioned data.
problem Generating synthetic data from vertically partitioned data while preserving privacy.
method Differentially private stochastic gradient descent (DP-SGD) algorithm combined with secure multiparty computation (MPC).
result Comparable accuracy to non-partitioned data, demonstrating privacy-preserving synthetic data generation.
Based on the proof of Labastida-Mari{ñ}o-Ooguri-Vafa conjecture \cite{lmov}, we derive an infinite product formula for Chern-Simons partition functions, the generating function of quantum $\fsl_N$ invariants. Some symmetry properties of the infinite product will also be discussed.
Norm-ranging LSH improves MIPS performance by addressing 2-norm distribution issues.
problem Long tails in 2-norm distribution of real datasets affect Simple-LSH performance.
method Norm-ranging LSH partitions datasets into sub-datasets and builds independent hash indexes.
result Norm-ranging LSH achieves an order of magnitude speedup over Simple-LSH.
ProductNet curates high-quality product datasets for better product understanding.
problem Lack of high-quality product datasets for product representation learning.
method Curated high-quality product datasets with a multi-modal deep neural network and active learning.
result Master model yields high categorization accuracy (94.7% top-1 accuracy for 1240 classes).
New algorithm improves partition function approximation for graphical models.
problem Computing partition function of graphical models is computationally hard.
method Spectral mean-field scheme using FPTAS for low-rank matrices, and approximation of high-rank matrices.
result The proposed algorithm is more robust and accurate than previous methods.
Based on the orthogonal Labastida-Mari{ñ}o-Ooguri-Vafa conjecture made by L. Chen & Q. Chen [5], we derive an infinite product formula for Chern-Simons partition functions, which generalizes the Liu-Peng's [19] recent results to the orthogonal case. Symmetry property of this new infinite product structure is also discu…
Improved supervised EM learning for shared kernel models with feature space partitioning.
problem Lack of rigour in EM derivation and high computational complexity.
method Detailed derivation of EM for Gaussian shared kernel model, feature space partitioning to reduce complexity.
result Improved performance at reduced complexity achieved.
Optimizes Lipschitz estimates for partitions of unity and characterizes spaces with Assouad-Nagata dimension.
problem Understanding the properties of partitions of unity and their Lipschitz bounds.
method Analyzes the standard partition of unity and its -generalizations, using the approximate midpoint property and Lebesgue number.
result Optimal Lipschitz bounds for partitions of unity and characterizes metric spaces with Assouad-Nagata dimension.
Method generates VaR scenarios for dependent risks under Solvency II.
problem Stress testing and VaR calculation for dependent risks.
method Monte Carlo simulation using product beta distributions.
result Direct scenario estimation of joint density from transformed data.
SBT model uses randomized sharding and sub-models to improve Bayesian Additive Regression Trees.
problem Improving efficiency and accuracy of Bayesian Additive Regression Trees.
method Randomized sharding, sub-models, intersection tree structure, optimal design.
result Theoretical optimal weights and worst-case complexity of SBT model.
Algorithms learn and test variable partitions in various groups and error metrics.
problem Learning and testing variable partitions in different groups and error metrics.
method Algorithms for agnostically learning and testing -partitionability over various groups and error metrics.
result Learning algorithms for -partitionability with polynomial time complexity and testing with adaptive queries.
Products of Hidden Markov Models(PoHMMs) are an interesting class of generative models which have received little attention since their introduction. This maybe in part due to their more computationally expensive gradient-based learning algorithm,and the intractability of computing the log likelihood of sequences under…
CwA optimizes search performance by jointly learning a balanced database partition and a neural probing function.
problem Suboptimal search performance due to mismatched database and query distributions.
method CwA jointly learns a balanced database partition and a neural probing function to optimize search performance directly for the query distribution.
result CwA achieves up to 4.7x throughput over state-of-the-art methods at equal recall.
Study of gauge theory blowups and Painlevé VI identity.
problem Understanding gauge theory blowups and their relation to Painlevé VI.
method Analyzing four-dimensional supersymmetric gauge theory with defects and proposing identities.
result Formula relating tau-function to conformal blocks of Liouville theory.
We propose a kernel method to identify finite mixtures of nonparametric product distributions. It is based on a Hilbert space embedding of the joint distribution. The rank of the constructed tensor is equal to the number of mixture components. We present an algorithm to recover the components by partitioning the data p…
Two tricks reduce LSTM complexity and speed up training.
problem Training large LSTM networks is computationally expensive.
method Matrix factorization and partitioning of LSTM components.
result Significantly faster training with fewer parameters.
A novel method clusters and analyzes categorical time series data.
problem Clustering and analyzing temporal event sequences data.
method Three-dimensional data grid models for 3D-co-clustering.
result Discover meaningful underlying patterns of categorical time series data.
We introduce partial secondary invariants associated to complete Riemannian metrics which have uniformly positive scalar curvature outside a prescribed subset on a spin manifold. These can be used to distinguish such Riemannian metrics up to concordance relative to the prescribed subset. We exhibit a general external p…
Paper proves consistency of spectral hypergraph partitioning under a new model.
problem Consistency of spectral hypergraph partitioning under a new model.
method Spectral hypergraph partitioning algorithm using matrix concentration inequalities.
result First consistency result for partitioning non-uniform hypergraphs.
Computes entanglement entropy using Chern-Simons theory and symmetric webs.
problem Determining if a product state implies unlinked components.
method Using symmetric webs to compute colored link invariants and write multi-partite entangled states.
result Written down multi-partite entangled states of any given link.
A method for identifying joint and individual subspaces from multi-view data.
problem Unclear conditions for reliably identifying joint and individual subspaces from noisy, high-dimensional measurements.
method Rigorously quantifies conditions based on signal rank, principal angles, and noise levels. Characterizes spectrum perturbations of product of projection matrices.
result Estimates joint and individual subspaces more accurately than existing approaches in simulations and real-world applications.
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star, Lie derivative, pullback and interior product. Partitions of unity exist in thi…
Shortcut Matrix Product States and its applicationscond-mat.stat-mech
A new model SMPS alleviates the exponential decay of correlations in MPS.
problem Exponential decay of correlations in Matrix Product States (MPS) limits their power in capturing long-range dependences.
method Introducing long-range interactions (shortcuts) to MPS to decrease correlation length while preserving computational efficiency.
result SMPS can decrease significantly the correlation length of MPS, improving its ability to capture long-range dependences.
A new method improves maximum inner product search by locally decomposing residual vectors.
problem Maximum inner product search efficiency and accuracy.
method Local Orthogonal Decomposition (LOD) combined with multiscale quantization.
result LOD consistently achieves higher recall than previous methods under the same bitrates.
Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary time, N=1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interprete…
Samplets and multiwavelets constructed from scattered data converge to specific densities in the limit.
problem Constructing data-adapted multiresolution analyses and multiwavelets with flexible vanishing moments.
method Probabilistic framework for samplet construction; convergence to multiwavelets with broken polynomial densities.
result Samplet construction converges to multiwavelets in the infinite data limit.
Developed a symplectic integrator for complex manifolds.
problem Simulating Hamiltonian systems on specific manifolds.
method Partitioned Runge--Kutta methods for Hamiltonian systems on products of Hamiltonian manifolds, with derived symplecticity conditions.
result Derived algebraic conditions for symplecticity of methods.
In this paper, we deal with the problem of curves clustering. We propose a nonparametric method which partitions the curves into clusters and discretizes the dimensions of the curve points into intervals. The cross-product of these partitions forms a data-grid which is obtained using a Bayesian model selection approach…
Localized signal representation on graph bundles using Fourier analysis.
problem Representing signals on graph bundles with twists.
method Partition of unity and product factorization over the base graph.
result Lifted bases for signal spaces of graph bundle components.
Rectangular Bounding Processstat.ML
Rectangular Bounding Process (RBP) improves partitioning efficiency in multi-dimensional spaces.
problem Creating many unnecessary divisions in sparse regions when describing dense regions.
method Introduces Rectangular Bounding Process (RBP) to efficiently partition multi-dimensional spaces using a bounding strategy.
result The RBP is self-consistent and can be extended to infinite space, offering rich yet parsimonious expressiveness.
The study sets performance limits for record linkage using KL divergence.
problem Efficiently merging records in large, noisy databases to remove duplicates.
method Assesses performance bounds using Kullback-Leibler divergence in a Bayesian record linkage framework.
result Provides upper and lower bounds on misclassification probability.
A-manifolds and A-bundles are manifolds and vector bundles modelled on a projective finitely generated module over a topological algebra A. In this paper we investigate the conditions under which an A-bundle is provided with an A-valued hermitian structure and a compatible connection, in case A is a commutative complet…
Efficiently calculates PL model likelihood for partitioned preference data.
problem Computational infeasibility of calculating PL model likelihood for partitioned preference data.
method Random utility model formulation and efficient numerical integration approach.
result Proposed method outperforms existing LTR baselines and scales to real-world tasks.
New basis for permutation equivariant layers reduces computation costs.
problem Efficiently computing permutation equivariant layers in neural networks.
method Generalized partition algebra basis with low-rank tensors.
result Low-rank tensors enable faster computation compared to orbit basis.
New invariants defined from 6d fivebrane theory BPS states.
problem Homological invariants of 3-manifolds.
method Physical system involving 6d fivebrane theory on 3-manifolds times a 2-disk.
result Hilbert space of BPS states categorifies various partition functions of 3d theories.
Let be a complete Riemannian manifold and assume that is partitioned by a hypersurface . In this paper we introduce a novel class of functions on noncompact manifolds, which is slightly larger than the algebra of Higson functions. Out of that belongs to we construc…