Improved sparse Gaussian processes using structured scaling matrices and Power-EP framework.
problem Scaling Gaussian processes for large datasets.
method Structured diagonal scaling matrix and Power-EP framework.
result Structured approximations improve performance without increasing computational cost.
Data mining reveals power structures in Bangladeshi newspapers.
problem Understanding the power dynamics and narrative structure in news reporting.
method Named entity recognition to create temporal actor networks from news statements.
result Cliquishness among powerful political leaders in news articles.
DeepGDL models create realistic power grids from confidential data.
problem Creating realistic power grids from confidential data.
method Graph distribution learning (GDL) with a deep nonlinear recurrent structure.
result DeepGDL models accurately create synthetic power grids.
The paper studies volumes of direct images for high tensor powers of ample bundles.
problem Understanding asymptotics of Monge-Ampère volumes for high tensor powers of ample line bundles.
method Analyzes the leading term of asymptotics and classifies bundles saturating a topological bound.
result Provides a characterization of bundles admitting projectively flat Hermitian structures in the case of high symmetric powers of ample vector bundles.
By use of a natural map introduced recently by the first and third authors from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the small differentiable deformation of this manifold, we will give a power series proof for Kodaira-Spencer's local stability theorem of Kä…
In this paper we propose a tractable quadratic programming formulation for calculating the equilibrium term structure of electricity prices. We rely on a theoretical model described in [21], but extend it so that it reflects actually traded electricity contracts, transaction costs and liquidity considerations. Our nume…
Study on expressive power of Euclidean kernels and efficient kernel learning.
problem Limiting the expressive power of kernel methods and improving kernel learning efficiency.
method Define Euclidean kernels, analyze their geometric and spectral properties, and develop efficient algorithms for kernel learning.
result Prove limitations on the expressive power of Euclidean kernels and derive efficient algorithms for kernel learning.
Paper detects and estimates breaks in high-dimensional functional time series.
problem Detecting and estimating structural breaks in heterogeneous mean functions of high-dimensional functional time series.
method Proposes a new test statistic combining functional CUSUM and power enhancement components, with a clustering algorithm for group structure estimation.
result The proposed techniques have satisfactory performance in finite samples, detecting and estimating breaks effectively.
GNNs are powerful but limited in their ability to distinguish certain graph structures.
problem Limited understanding of GNNs' representational properties and limitations.
method Theoretical framework and analysis of GNN expressive power, development of a provably most expressive GNN architecture.
result GNNs cannot learn to distinguish certain simple graph structures, but a new architecture can.
Power quandles improve group invariants and allow group presentations.
problem Understanding and classifying groups using algebraic structures.
method Introducing power quandles, which retain conjugation and power maps, and showing their effectiveness in group theory.
result Power quandles determine central quotients and centers of groups, and can approximate any group.
A strategy for spectrum sharing in CRNs with multiple PT power levels.
problem Efficient spectrum usage for secondary users in CRNs with multiple PT power levels.
method Data-driven/machine learning based multi-level spectrum sensing and prediction-transmission structures.
result The proposed strategy effectively aligns the ST with the PT power levels, improving spectrum usage.
Paper examines the structure of stochastic gradients in deep learning.
problem Exploring the structure and heavy tails of stochastic gradients in deep learning.
method Conducted formal statistical tests on stochastic gradients and gradient noise.
result Stochastic gradients and gradient noise do not exhibit power-law heavy tails, but their covariance spectra do.
Method detects critical events in complex systems by learning latent causal structure.
problem Detecting onset of epileptic seizures, customer churn, or pandemics from hidden causal interactions.
method A machine learning method that learns an optimal feature representation from powers of the empirical covariance or precision matrix.
result Proves structural consistency and demonstrates competitive results in seizure and churn prediction.
Bitcoin price shows both chaos and order, with multi-scale correlation structure.
problem Tackles the efficiency of the Bitcoin market.
method Uses novel tools for multi-fractal properties estimation.
result Bitcoin price exhibits multi-scale correlation structure with power-law behavior.
Proposes a new complex Gaussian distribution for better modeling of complex-valued signals.
problem Limited ability of Gaussian distribution to represent diverse amplitude characteristics.
method Introduces a power-weighted noncentral complex Gaussian distribution on the complex plane.
result Consistently outperforms conventional distributions in log-likelihood for speech power spectra.
The study examines power quotients of surface groups and mapping class groups, proving structural properties and isomorphisms.
problem Structural properties and isomorphisms of power quotients of surface groups and mapping class groups.
method Analyzes the outer automorphism and automorphism groups of power quotients, proving isomorphisms and structural properties.
result The outer automorphism group of Γ(n) is isomorphic to the quotient of the extended mapping class group of S by nth powers of Dehn twists. Study characteristic classes for TC structures on principal G-bundles.
problem Classifying principal G-bundles with TC structures.
method Algebraic-geometric construction using power maps on BcomG. result Construction of characteristic classes for TC structures on SU(n), U(n), and Sp(n) bundles. Unified theory for neural scaling laws in hierarchically compositional data.
problem Understanding neural scaling laws in hierarchically compositional data.
method Probabilistic context-free grammars and power-law distributed production rules.
result Unified learning curve behavior for classification and next-token prediction tasks.
We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge to zero for power laws o…
CW Networks leverage cell complexes to enhance GNNs, achieving state-of-the-art results on molecular datasets.
problem Graph Neural Networks struggle with long-range interactions and lack principled ways to model higher-order structures.
method CW Networks use cell complexes to decouple computational and input graph structures, enabling flexible hierarchical message passing.
result CW Networks achieve state-of-the-art results on molecular datasets.
Distribution grid is the medium and low voltage part of a large power system. Structurally, the majority of distribution networks operate radially, such that energized lines form a collection of trees, i.e. forest, with a substation being at the root of any tree. The operational topology/forest may change from time to …
Maximizing the speed and precision of communication while minimizing power dissipation is a fundamental engineering design goal. Also, biological systems achieve remarkable speed, precision and power efficiency using poorly understood physical design principles. Powerful theories like information theory and thermodynam…
It is studied a 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant. On such a manifold a fundamental tensor by the metric and by the covariant derivative of…
PPI uses proxy data to improve inference from limited labels across related tasks.
problem Statistical inference with limited labels across multiple related tasks.
method Prediction-powered inference framework that uses cross-task recalibration to improve power and accuracy.
result Cross-task recalibration can substantially reduce confidence interval widths when labels are scarce.
Power-law spectrum of random feature model is preserved in neural networks.
problem Preserving power-law spectrum in neural networks through random feature model.
method Characterized eigenvalues of population random-feature covariance using dyadic head-tail decomposition and Wick chaos expansions.
result Power-law exponent α is inherited from input covariance, modified by a logarithmic correction. Estimates statistical power for cluster analysis in biomedical research.
problem Lack of established methods to compute a priori statistical power for cluster analysis.
method Simulation studies varying subgroup size, number, separation, and covariance structure.
result Sufficient statistical power achieved with small samples (N=20-30) for large effect sizes.
Racks and quandles are rich algebraic structures that are strong enough to classify knots. Here we develop several fundamental categorical aspects of the theories of racks and quandles and their relation to the theory of permutations. In particular, we compute the centers of the categories and describe power operations…
For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Guillemin-Uribe showed that there is a well-defined cluster of low-lying eigenvalues, whose distribution is described by a spectral density fun…
Paper tackles RL for power grid topology optimization.
problem Managing large action spaces in growing power networks.
method Hierarchical multi-agent reinforcement learning (MARL) framework.
result MARL framework outperforms single-agent RL methods.
Survey of RL methods for optimizing power grid topologies.
problem Optimizing power grid operation with adaptive control strategies.
method Reinforcement Learning (RL) for dynamic and uncertain environments.
result Comprehensive evaluation of RL-based methods for power grid topology optimization.
This work establishes properties on diffeological structures for set-valued maps and measures.
problem Establish rigorous properties on diffeological structures for set-valued maps and measures.
method Using diffeologies, the authors link various structures including set-valued maps, relations, gradients, measures, and shape analysis.
result Established rigorous properties on sample diffeologies.
Model shows financial turbulence similar to turbulence, with wealth cascading from large to small entities.
problem Understanding wealth distribution and dynamics in financial systems.
method Constructed a multiscale model for hierarchical financial structures.
result Found wealth distribution exhibits power law at large scales and Maxwellian at small scales.
A deep learning method speeds up probabilistic optimal power flow calculations.
problem Efficiently solving large-scale nonlinear and nonconvex optimization problems in power systems.
method Developed a SDAE-based OPF using stacked denoising auto encoders to extract system correlations and calculate OPF solutions.
result The trained SDAE network can quickly compute OPF solutions for random system states without optimization.
Unified CI test for categorical and ordinal data maintains power in high dimensions.
problem Rapid degradation of statistical power in existing CI tests for high-dimensional conditioning variables.
method Unified CI test for categorical and ordinal data, maintaining reasonable calibration and power in high dimensions.
result Our test outperforms existing baselines in model testing and structure learning for dense directed graphical models.
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly point to invariants, that pinpoint intrinsic properties of the data and of the …
By use of a natural extension map and a power series method, we obtain a local stability theorem for p-Kähler structures with the (p,p+1)-th mild ∂∂ˉ-lemma under small differentiable deformations.
We report empirical studies on the personal income distribution, and clarify that the distribution pattern of the lognormal with power law tail is the universal structure. We analyze the temporal change of Pareto index and Gibrat index to investigate the change of the inequality of the income distribution. In addition …
Graph Attention Networks predict power outage durations from natural disasters.
problem Accurately predicting power outage durations from geospatial and weather data.
method Graph Attention Networks (GAT) for semi-supervised learning.
result GAT model outperforms existing methods by 2% - 15% in accuracy.
We study power-law correlations properties of the Google search queries for Dow Jones Industrial Average (DJIA) component stocks. Examining the daily data of the searched terms with a combination of the rescaled range and rescaled variance tests together with the detrended fluctuation analysis, we show that the searche…
MoEs can efficiently model complex tasks with low-dimensionality and sparsity.
problem Understanding the theoretical foundations of MoEs for complex tasks.
method Systematic study of MoEs with two structural priors: low-dimensionality and sparsity.
result MoEs can approximate functions on low-dimensional manifolds and exhibit exponential structured tasks.
Cross-prediction improves inference from small labeled datasets.
problem Valid inference from small labeled datasets with imperfect predictions.
method Imputes missing labels via machine learning and debiases predictions.
result Inferences achieve desired error probability and are more powerful.
Morphological neurons are powerful and versatile for classification and regression problems.
problem Designing effective sequences of morphological operations and structuring elements.
method Theoretical analysis of morphological neurons as a sum of hinge functions, and their effectiveness in approximating any continuous function.
result Morphological neurons are more powerful than previously anticipated and can approximate any continuous function.
New method estimates causal effects in complex spaces using topological structures.
problem Challenges in estimating causal effects in non-Euclidean spaces.
method Developed a topological causal inference framework using power-weighted silhouette functions of persistence diagrams.
result Successfully quantifies topological treatment effects across various complex outcomes.
New analysis shows over-squashing limits GNNs' power.
problem Understanding the expressive power of GNNs, especially under over-squashing.
method Quantitative measure of pairwise interactions in MPNNs, proving capacity requirements.
result Over-squashing hinders GNNs' ability to learn complex node feature functions.
We present a model for random simple graphs with a degree distribution that obeys a power law (i.e., is heavy-tailed). To attain this behavior, the edge probabilities in the graph are constructed from Bertoin-Fujita-Roynette-Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the c…
Proposes a new method for high-dimensional data analysis.
problem Sparse PCA limitations in high-dimensional data analysis.
method Low-rank principal eigenmatrix analysis, matricized rank-truncated power method.
result Competitive empirical performance in synthetic data sets.
In this paper we propose a quadratic programming model that can be used for calculating the term structure of electricity prices while explicitly modeling startup costs of power plants. In contrast to other approaches presented in the literature, we incorporate the startup costs in a mathematically rigorous manner with…
The well known conformal covariance of the Dirac operator acting on spinor fields over a semi Riemannian spin manifold does not extend to powers thereof in general. For odd powers one has to add lower order curvature correction terms in order to obtain conformal covariance. We derive an algorithmic construction in term…