Paper introduces signal processing on cell complexes.
problem Processing signals on non-Euclidean domains.
method Signal processing on abstract regular cell complexes.
result Hodge Laplacians for cell complexes enable convolutional filters.
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48 results for “Complex Processes”
Signatures of Infinity: Nonergodicity and Resource Scaling in Prediction, Complexity, and Learningcond-mat.stat-mech
We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit problem. We contrast our analysis with computation-theoretic and statistical infer…
Tutorials on signal processing on higher-order networks like simplicial complexes and hypergraphs.
problem Processing complex data structures with polyadic relationships.
method Introduction to simplicial complexes and hypergraphs, Fourier analysis, signal denoising, interpolation, embeddings, neural networks.
result Multi-relational operators like the Hodge Laplacian for simplicial complexes and tensor representations for hypergraphs.
Improved sample complexity for Gaussian process approximations.
problem Efficiently approximating Gaussian processes with sparse spectrum.
method Improved sample complexity analysis and auto-encoding algorithm.
result Gaussian process predictions and model evidence can be well-approximated with low sample complexity.
A new algorithm splits Gaussian processes for efficient streaming data.
problem Poor scaling of Gaussian processes in streaming data.
method Sequential partitioning of input space and localized Gaussian process fitting.
result The algorithm achieves linear memory complexity and superior time and space complexity.
Deep learning improves analysis of complex natural processes.
problem Simplistic dynamics in regression analyses of complex natural processes.
method Flexible function approximation using deep learning, relaxing standard assumptions.
result Substantial improvements in behavioral and neuroimaging data.
The paper extends Gaussian processes to model complex interactions in cellular complexes.
problem Capturing topological inductive biases in machine learning models.
method Proposes Gaussian processes on cellular complexes, introducing novel kernels.
result Derives two novel kernels for modeling interactions between cells.
RML improves generative modeling of complex distributions.
problem Learning complex distributions in applications.
method RML defines a forward process to a known distribution, then learns a reverse Markov process.
result RML efficiently captures complex distributions in simulations and climate data.
This work introduces a new model for complex stochastic processes.
problem Difficulties in representing non-stationary distributions with conventional models.
method Recurrent Autoregressive Flows using normalizing flows with recurrent neural connections.
result Demonstrates the effectiveness of the proposed model through experiments.
VSE estimates complex processes from noisy measurements without a model.
problem Estimating states of complex, model-free processes from noisy data.
method Variational state estimation using recurrent neural networks (RNNs) in both learning and inference phases.
result VSE provides a competitive state estimate for a benchmark process (Lorenz system) compared to known and data-driven methods.
Study shows cognitive load impacts financial market efficiency, especially for less sophisticated investors.
problem Cognitive load's effect on financial market information processing.
method Developed a theoretical framework and tested it with exogenous disclosure complexity variation.
result Cognitive load significantly impairs price discovery, particularly for less sophisticated investors.
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process is uncorrelated with its complex conjugate. This assumption is a good model of th…
New algorithms extract low-dimensional representations from sequential data, revealing insights into complex processes.
problem Challenges in extracting low-dimensional representations from sequential, high-dimensional, sparse, and noisy data.
method Developed new clustering algorithms based on Block Markov Chains theory, validated on real-world data.
result These algorithms can successfully extract low-dimensional representations from real-world sequential data, revealing insights into complex processes.
Improved Gaussian process experts model for complex data.
problem Limitations of standard Gaussian processes: scalability and predictive performance.
method Proposes a new mixture model of Gaussian process experts based on kernel stick-breaking processes.
result Improved predictive performance compared to existing models.
Paper introduces a neural network-based non-stationary influence kernel for complex event data.
problem Modeling complex, non-stationary, and dependent discrete event data.
method Neural Spectral Marked Point Processes (NSMPP) with a versatile non-stationary influence kernel.
result NSMPP outperforms state-of-the-art models on synthetic and real data.
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data, standard strategies for sparsifying the model can prevent the approximation of …
Proposes a new model for complex multivariate event data.
problem Modeling complex multivariate event data with spatio-temporal dynamics.
method Integrates spatial information into latent state evolution through learned temporal and spatial decay dynamics.
result Successfully recovers sensible temporal and spatial intensity structure in multivariate spatio-temporal point patterns.
New method reduces sample complexity for learning Ising model dynamics exponentially.
problem Learning binary graphical models from correlated samples produced by a dynamical process.
method Two estimators based on interaction screening objective and conditional likelihood loss.
result Sample complexity reduces exponentially for samples from a dynamical process far from equilibrium.
We develop a complexity measure for large-scale economic systems based on Shannon's concept of entropy. By adopting Leontief's perspective of the production process as a circular flow, we formulate the process as a Markov chain. Then we derive a measure of economic complexity as the average number of bits required to e…
Study differentially private methods for learning Hawkes processes.
problem Lack of thorough analysis on sample complexity for learning Hawkes processes parameters and releasing differentially private versions.
method Developed non-private and differentially private estimators for Hawkes processes parameters.
result Obtained sample complexity results for both private and non-private settings.
The paper proposes a deep generative model for complex disease trajectories.
problem Modeling and analyzing complex disease trajectories.
method Deep generative time series approach with semi-supervised latent processes.
result The model can discover novel aspects of diseases and cluster them into new sub-types.
Complex numbers have long been favoured for digital signal processing, yet complex representations rarely appear in deep learning architectures. RNNs, widely used to process time series and sequence information, could greatly benefit from complex representations. We present a novel complex gated recurrent cell, which i…
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic gene…
New algorithm reduces sample complexity for planning in MDPs.
problem Planning in MDPs with unknown transitions.
method MDP-GapE, a trajectory-based MCTS algorithm.
result Proves upper bound on sample complexity in terms of sub-optimality gaps.
Inspired by constructions in complex geometry we introduce a thermodynamic framework for Monge-Ampère equations on real tori. We show convergence in law of the associated point processes and explain connections to complex Monge-Ampère equations and optimal transport.
Unified framework for inference in complex nonlinear processes.
problem Challenges in inferring nonlinear continuous stochastic processes with sparse observations and complex topologies.
method Neural Backward Filtering Forward Guiding (NBFFG) framework that constructs a variational posterior using a proxy linear-Gaussian process.
result Empirical results show NBFFG outperforms baselines on synthetic benchmarks and high-dimensional phylogenetic analysis tasks.
Optimal Sample Complexity of Reinforcement Learning for Mixing Discounted Markov Decision Processescs.LG
New RL theory reduces sample complexity for mixing MDPs.
problem Optimal sample complexity for reinforcement learning in mixing MDPs.
method Regeneration-type ideas to analyze mixing times.
result Optimal sample complexity depends on mixing time, not just discount factor.
Survey of complex-valued neural networks for improved performance.
problem Lack of complex-valued neural networks in machine learning frameworks.
method Literature review of CVNNs.
result Advantages of CVNNs over real-valued neural networks.
Brownian motion and stochastic areas on complex partial flag manifolds with blocks of equal sizemath.PR
This paper constructs Brownian motion on complex flag manifolds and finds joint distribution of stochastic areas.
problem Modeling stochastic areas on complex partial flag manifolds.
method Constructs Brownian motion on complex partial flag manifolds and uses it to find joint distribution of stochastic areas.
result Limit law of stochastic areas is a multivariate Cauchy distribution.
Improved model for non-smooth signals with complex spectra.
problem Current models struggle with non-smooth signals and complex spectral structures.
method CGPCM and RGPCM models with causality and Bayesian nonparametric interpretations, improved variational inference.
result Proposed models show better performance on synthetic and real-world data.
Continuous process closes cusps in complex algebraic surfaces.
problem Developing cusps in Kähler-Einstein metrics on algebraic surfaces.
method Continuous cusp closing process via gluing construction.
result Cusps form in Kähler-Einstein metrics near isolated singularities.
Percolation on complex networks has been used to study computer viruses, epidemics, and other casual processes. Here, we present conditions for the existence of a network specific, observation dependent, phase transition in the updated posterior of node states resulting from actively monitoring the network. Since tradi…
This paper reconstructs complex graph signals using kernel methods on manifolds.
problem Reconstructing complex graph signals from samples on graph vertices.
method Kernel methods on complex manifolds, embedding vertices into higher-dimensional spaces.
result Effective reconstruction of complex graph signals, outperforming conventional methods.
VOGP efficiently identifies Pareto optimal solutions in black-box vector optimization.
problem Black-box vector optimization with incomplete order relations.
method VOGP is an adaptive elimination algorithm using Gaussian process bandits.
result VOGP achieves theoretical guarantees with sample complexity bounds.
Neural Diffusion Processesstat.ML
NDPs learn to sample from complex function distributions using neural networks and diffusion models.
problem Learning rich distributions over functions with neural networks.
method NDPs use denoising diffusion models and custom attention blocks to incorporate stochastic process properties.
result NDPs can capture functional distributions close to true Bayesian posteriors and outperform neural processes.
Deep Gaussian processes on manifolds improve performance on complex data.
problem Complex data on manifolds that shallow models struggle with.
method Residual deep Gaussian processes on Riemannian manifolds.
result Significant improvement in prediction quality and uncertainty calibration.
HNP3: A Hierarchical Nonparametric Point Process for Modeling Content Diffusion over Social Mediastat.ML
This paper introduces a novel framework for modeling temporal events with complex longitudinal dependency that are generated by dependent sources. This framework takes advantage of multidimensional point processes for modeling time of events. The intensity function of the proposed process is a mixture of intensities, a…
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding literature. The method can be performed in operations, where…
A novel nonstationary permanental process relaxes kernel constraints and captures complex data patterns.
problem Limitations of existing permanental processes in terms of kernel types and stationarity.
method Sparse spectral representation of nonstationary kernels and hierarchical stacking of spectral feature mappings.
result Enhanced model expressiveness and reduced computational complexity.
New phase harmonic covariance models capture non-Gaussian properties of stationary processes.
problem Capturing non-Gaussian properties of stationary processes using Fourier phase.
method Introduce phase harmonic covariance moments and maximum entropy models conditioned by these moments.
result Maximum entropy models from phase harmonic covariances improve image synthesis of turbulent flows.
ETGPSSM efficiently models high-dimensional, non-stationary systems with reduced complexity.
problem Prohibitive computational and parametric complexity in high-dimensional, non-stationary dynamical systems.
method ETGPSSM integrates a single shared GP with input-dependent normalizing flows for scalable and flexible modeling.
result ETGPSSM outperforms existing models in computational efficiency and accuracy.
Framework integrates Markov and causal models for accurate counterfactual inference.
problem Lack of counterfactual inference in Markov models and identification in causal models.
method Defines structural causal models in terms of Markov process parameters and equilibrium dynamics, enabling consistent counterfactual inference.
result Proposed framework alleviates identifiability issues and improves accuracy of counterfactual inference.
Formalizes identifying information to answer key questions about machine learning from uncertain and novel observations.
problem Understanding and quantifying information from uncertain and novel observations in machine learning.
method Formalizes identifying information, defines hypothesis identification and sample complexity, and proves sample complexity properties for various data-generating processes.
result Proves the information theoretic characteristics of hypothesis identification and sample complexity, and shows how to compute identifying information and novel information.
Develops scalable model for learning velocity fields in complex traffic scenarios.
problem Learning heterogeneous and dynamic velocity fields in complex traffic scenarios.
method Nonparametric Bayesian modeling with hierarchical Dirichlet process and infinite hidden Markov model, Gaussian process prior, and scalable approximate inference.
result Demonstrates effective scalability and applicability to real-world traffic data.
A Low Complexity Decentralized Neural Net with Centralized Equivalence using Layer-wise Learningcs.LG
Low complexity decentralized neural net with centralized performance.
problem Training large neural networks in distributed nodes without data sharing.
method Layer-wise learning using ADMM for low complexity and centralized performance.
result Equivalent learning performance to centralized training in distributed nodes.
A new method for efficient Gaussian process regression reduces complexity and improves scalability.
problem Efficient Gaussian process regression for large datasets.
method Learnable coreset-based variational inference for Gaussian processes.
result CVGP reduces the dimensionality of the variational parameter search space to linear complexity.
A new model captures complex event data using attention and Fourier kernels.
problem Capturing complex non-linear temporal dependencies in discrete event data.
method Integrates attention mechanism into point processes' conditional intensity function and uses Fourier kernel embedding.
result Established theoretical properties and demonstrated competitive performance.
Majorizing measures control sequential complexities for online learning.
problem Extending classical empirical processes theory to sequential cases.
method Generic chaining, majorizing measures, fractional covering numbers.
result Sharp control of worst-case sequential Rademacher complexity.