Extends ambient modules to hidden space for better generative model training.
problem Lack of practical methods for applying ambient modules to hidden space of generators.
method Extend ambient modules to hidden space, provide uniqueness condition and strategy.
result Practical method for ambient hidden generator in adversarial training process.
A new clustering method learns shared hidden space and fuzzy partition between multi-view data.
problem Effective exploitation of relationship between different views in multi-view data.
method Hidden space sharing multi-view fuzzy clustering (HSS-MVFC) method based on fuzzy c-means.
result The proposed method outperforms many related clustering methods in experiments.
A new method assigns hidden parameters deterministically to improve learning efficiency.
problem Traditional learning methods struggle with high computational burden.
method Two-stage learning with deterministic assignment of hidden parameters.
result Deterministic assignment of hidden parameters almost matches traditional learning's generalization performance.
Paper addresses hidden faces in configuration space integrals for embeddings.
problem Understanding hidden faces in configuration space integrals for long embeddings.
method Modified configuration space integrals incorporating acyclic bar complex of a dg algebra.
result Cochain map from new graph complex to de Rham complex of embeddings modulo immersions.
Spectral method learns hidden state mapping for RL in rich-observation MDPs.
problem Challenges in RL with large state spaces and hidden low-dimensional structure.
method Spectral decomposition method to learn hidden state to observation state mapping.
result Achieves low regret with weak dependence on observed space dimensionality.
Study spectral settings of generalized Laplacians on homogeneous spaces.
problem Understanding the spectral properties of generalized Laplacians on compact homogeneous spaces.
method Investigates the generic spectral configuration of operators on G-invariant metrics on M=G/K. result The spectral setting depends on G-isometries and hidden symmetries. The hidden M-algebra is integrated into a super-Lie group, allowing for compactification of extra dimensions.
problem Integrating the hidden M-algebra into a super-Lie group to model super-exceptional spacetimes.
method Left-invariant extension of the decomposed M-theory 3-form, providing a computer-checked re-derivation and streamlined conception of super-Lie groups.
result Lattice subgroups of the hidden M-group allow toroidal compactification of hidden dimensions, akin to topological T-duality.
Proposes MV-Co-VH for multi-view clustering using visible and hidden views.
problem Lack of efficient algorithms for fully utilizing multi-view data.
method Projects multiple views to a common hidden space using NMF, then applies collaborative learning.
result Competitive clustering performance on UCI and real-world datasets.
New algorithm processes Riemannian data more efficiently.
problem High memory usage and slow speed in previous Riemannian HMMs.
method Online algorithm based on Baum-Welch adapted for Riemannian manifolds.
result Significant improvements in speed and efficiency.
New findings on hidden symmetries in ReLU networks.
problem Understanding the redundancy and symmetries in ReLU network parameter space.
method Analyzing parameter settings and function classes for various network architectures.
result For certain network architectures, there are no hidden symmetries.
Two-hidden-layer networks can approximate any continuous function.
problem Proving the universal approximation property of two-hidden-layer feedforward neural networks.
method Constructive approach based on simplicial maps and triangulations.
result Concrete architecture and weights can be obtained for approximating continuous functions.
Paper tackles hidden game problem in AI alignment and language games.
problem Hidden game problem in AI alignment and language games.
method Developed a composition of regret minimization techniques to discover and exploit hidden structures.
result Achieved optimal external and swap regret bounds for rapid convergence to correlated equilibria.
Paper analyzes coexisting hidden and self-excited attractors in an economic system.
problem Existence of coexisting hidden and self-excited attractors in economic systems.
method Integer and fractional order analysis of an economic system.
result Integer-order system exhibits multiple combinations of coexisting hidden and self-excited attractors.
The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same {\em special geometry} that is known from nonlinear sigma models in N=2 supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces…
Neural networks learn more efficiently with hidden factorial structures.
problem Challenges in high-dimensional statistical learning.
method Controlled experimental framework to test neural networks' ability to exploit hidden factorial structures.
result Neural networks can leverage hidden factorial structures to learn discrete distributions more efficiently.
Paper presents a fast method for estimating hidden states in Bayesian models.
problem Estimating hidden states in Bayesian state space models efficiently.
method Amortized simulation-based inference with pretraining.
result The method achieves sufficient accuracy and fast inference times.
Improves deep networks' robustness to adversarial attacks.
problem Deep networks' failure to perform well on data different from training distribution.
method Fortifies hidden layers by mapping them back to parts of the data manifold where the network performs well.
result Improves robustness to adversarial attacks in both black-box and white-box threat models.
This work speeds up fHMM analysis by tensor algebra.
problem Scalability issues in analyzing factorial hidden Markov models.
method Tensorized algorithms and scalable filtering methods.
result Significant improvement in computational performance.
QATS efficiently decodes HMMs with polylogarithmic complexity.
problem Efficiently decoding hidden Markov models from noisy observations.
method Divide-and-conquer procedure with polylogarithmic sequence complexity and cubic state space complexity.
result QATS outperforms Viterbi and PMAP in speed and accuracy.
Improves neural net generalization by modeling hidden state distribution.
problem Brittleness and failure of existing neural nets, especially with sparse labeled data and adversarial training.
method State reification: modeling hidden state distribution and projecting test states towards it.
result Helps neural nets generalize better, especially with sparse labeled data and adversarial training.
Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects: (A) global analysis on X by using representations of G (hidden symmetry); (B) global analysis on X by using representat…
New algorithm for aggregate inference in HMMs with continuous observations.
problem Inference in large populations with indistinguishable individuals and continuous measurements.
method Continuous observation collective forward-backward algorithm extending existing discrete case algorithm.
result Efficacy demonstrated through numerical experiments.
A new metric space model for point process excitations uncovers hidden interactions.
problem Estimating pairwise interactions in multivariate Hawkes processes is often infeasible.
method Developed a Hidden Hawkes Geometry (HHG) model to embed event types in a metric space.
result Learning the embedding reveals salient interactions in various applications.
Generalizes bits back coding for time-series models with latent Markov structures.
problem Efficiently compressing time-series data with latent Markov structures.
method Extends bits back coding to time-series models with latent Markov structures, including HMMs and LGSSMs.
result Effective for small scale models, promising for larger scale settings like video compression.
Study evaluates initialization strategies for infinite hidden Markov models.
problem Limited attention to initialization in infinite hidden Markov models.
method Systematically evaluated distance-based clustering, model-based, and uniform initializations.
result Distance-based clustering initializations consistently outperform other methods.
The generic identification problem is to decide whether a stochastic process (Xt) is a hidden Markov process and if yes to infer its parameters for all but a subset of parametrizations that form a lower-dimensional subvariety in parameter space. Partial answers so far available depend on extra assumptions on the pro…
New approach finds optimal hidden paths in large models, scaling to high dimensions.
problem Finding optimal hidden paths in large, high-dimensional models.
method Developed a new approach to existence of the infinite Viterbi alignment for models satisfying a decay-convexity condition.
result Quantitative bounds on the distance to the infinite Viterbi alignment, demonstrating scalability to high-dimensional problems.
New algorithm learns HMM parameters on Riemannian manifolds.
problem Learning hidden Markov models on non-Euclidean spaces.
method Geometric method of moments algorithm for Riemannian manifolds.
result Significantly improved speed and accuracy compared to existing methods.
Extends HMM to topological spaces for modeling complex data.
problem Modeling complex, continuous data in infinite-dimensional spaces.
method Use of Onsager-Machlup functional and Cameron-Martin space.
result Demonstrates versatility in identifying sleep states and snowfall patterns.
Enhances HiP-MDP for scalable, robust transfer learning.
problem Scalability and robustness in transfer learning for complex tasks.
method Introduces HiP-MDP with latent embeddings, Bayesian Neural Network, and scalable inference.
result Improved scalability and robustness in transfer learning for high-dimensional tasks.
Models improve syntactic clustering by adding more translation and part-of-speech decoders.
problem Improving syntactic saliency in hidden sentence representations.
method Training multi-task autoencoders on linguistic tasks and analyzing the learned hidden representations.
result The representation space becomes less entangled with more decoders, leading to better syntactic clustering.
HiP-MDPs help personalize HIV treatment across patient variations.
problem Physiological variation leads to different responses to treatments.
method Embed tasks in a low-dimensional space, updating HiP-MDP framework.
result Robust personalized medicine strategies developed for HIV treatment.
New estimators for causal effects in DAGs with hidden variables, addressing computational and statistical challenges.
problem Estimating causal effects in DAGs with hidden variables beyond traditional criteria.
method Introduces novel one-step corrected plug-in and targeted minimum loss-based estimators for causal effects in DAGs with hidden variables.
result Root-n consistent causal effect estimates with desirable statistical properties.
We briefly review the hierarchy for the hyper-Kähler equations and define a notion of symmetry for solutions of this hierarchy. A four-dimensional hyper-Kähler metric admits a hidden symmetry if it embeds into a hierarchy with a symmetry. It is shown that a hyper-Kähler metric admits a hidden symmetry if it admits a ce…
Study generalizes Yang-Mills equations for special complex surfaces.
problem Deriving equations for self-dual Yang-Mills fields on complex surfaces.
method Generalization of flat space Yang's and Newman's equations to conformally Kahler Riemannian 4-manifolds.
result Continuous group of hidden symmetries found only for conformally half-flat geometry.
A method for generating random weights and biases in neural networks with random hidden nodes.
problem The need for a method to control the generalization degree of neural networks with random hidden nodes.
method Proposes a method to generate random weights and biases that depend on input data range and activation function type.
result Improves the approximation performance of neural networks with random hidden nodes.
The paper tackles estimation of hidden state LTI systems of unknown order.
problem Estimation of Markov parameters and minimal realization of unknown order LTI systems.
method Hankel penalized least square estimator, Ho-Kalman algorithm, and a combined algorithm.
result Statistical guarantees for estimation error, rank recovery, and sample complexity.
Enhances sampling for complex hidden Markov models using ensemble MCMC.
problem Challenges in Bayesian inference for factorial hidden Markov models due to large latent variable space.
method Introduces ensemble MCMC with parallel tempering and genetic algorithm for efficient exploration.
result Improves sampling efficiency and mixing of existing samplers in various applications.
This paper introduces a new approach to finding knots and links with hidden symmetries using "hidden extensions", a class of hidden symmetries defined here. We exhibit a family of tangle complements in the ball whose boundaries have symmetries with hidden extensions, then we further extend these to hidden symmetries of…
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may not be able to model the complexities of a time series, while a large number of …
New model for bandit problem with linear rewards and side information.
problem Hidden Markovian bandit problem with linear rewards and side information.
method Presented a model and algorithm with regret analysis for the problem.
result Logarithmic regret achieved even in high-dimensional problems with structural side information.
Polynomial delay algorithm tests causal models with hidden variables.
problem Testing causal models with hidden variables in polynomial delay.
method c-component local Markov property (C-LMP) and polynomial delay algorithm.
result First algorithm for poly-delay testing of CIs in causal graphs with hidden variables.
The study analyzes local minima in ReLU networks and finds low probability of bad local minima.
problem Understanding the existence and probability of local minima in ReLU networks.
method Theoretical analysis combined with linear programming and experiments on MNIST and CIFAR-10 datasets.
result No bad differentiable local minima found almost everywhere in weight space.
Paper studies shallow ReLU networks' approximation rates for Hölder functions.
problem Understanding shallow ReLU networks' efficiency in approximating Hölder functions.
method Analyzes rates of uniform approximation by ReLU shallow neural networks with m hidden neurons. result Shows ReLU shallow neural networks can uniformly approximate Hölder functions with rates close to optimal.
Efficiently infers coupled hidden Markov models with noisy discrete observations.
problem Intractable inference for coupled continuous-time Markov chains with discrete observations.
method Latent Interacting Particle Systems, look-ahead functions, twisted Sequential Monte Carlo sampling.
result Demonstrated effectiveness on latent SIRS model and wildfire spread dynamics.
New method infers hidden states in continuous-time phenomena better than traditional models.
problem Traditional HSMM's are limited to discrete time grids and cannot handle irregularly spaced data.
method Formulated integro-differential forward and backward equations for CTSMC's, introduced scalable Viterbi-type algorithm.
result Efficiently solved equations for posterior marginals and path estimates.
Proves a central limit theorem for neural networks with hidden layers.
problem Understanding the statistical behavior of neural networks with large numbers of hidden units and training iterations.
method Rigorous mathematical proof using weak convergence methods and stochastic analysis.
result Neural network fluctuations around mean-field limit follow a Gaussian distribution and satisfy a stochastic partial differential equation.
Deep kernelized autoencoder maps inputs to kernel space for better representation learning.
problem Learning meaningful representations in high-dimensional data.
method Traditional autoencoder with new unsupervised loss function for kernel alignment.
result Kernel alignment controls hidden representation, improving reconstruction and kernel alignment.