Generative Stochastic Networks (GSNs) have been recently introduced as an alternative to traditional probabilistic modeling: instead of parametrizing the data distribution directly, one parametrizes a transition operator for a Markov chain whose stationary distribution is an estimator of the data generating distributio…
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48 results for “transition distributions”
Classifies special geometric distributions.
problem Classifying homogeneous real (2,3,5) distributions.
method Multiply transitive classification up to local diffeomorphism.
result Classified multiply transitive homogeneous real (2,3,5) distributions.
CtrlNS learns latent factors and distribution shifts from sparse transitions without prior knowledge.
problem Lack of prior knowledge of domain variables limits causal temporal representation learning.
method Sparse transition assumption and identifiability results from theoretical perspective.
result Effective in identifying distribution shifts and latent factors without prior knowledge.
A method for learning transition models in uncertain domains using relational rules and neural networks.
problem Learning transition models in complex, uncertain domains.
method Relational rules, greedy algorithm, neural networks.
result The method is more versatile and sample efficient than monolithic models.
Classifies multiply-transitive (2,3,5)-distributions using modern Cartan geometry.
problem Classifying multiply-transitive -distributions.
method Modern Cartan-geometric approach, incorporating structure theory.
result Complete classifications in both complex and real settings, with full curvature and infinitesimal holonomy.
A new method for ILO with transition model disparity using an intermediary policy.
problem Learning tasks from expert observations with different transition dynamics.
method Training an intermediary policy to match the state transitions of the expert dataset.
result Our method outperforms existing ILO approaches with transition model mismatch.
Estimates stationary distribution from batch transitions without access to the underlying process.
problem Estimating stationary distribution from batch transitions without access to the underlying process.
method Proposes a consistent estimator based on a correction ratio function and variational power method (VPM).
result VPM provides significantly better estimates across various problems.
Study of symmetry distributions in Lorentzian naturally reductive nilmanifolds.
problem Understanding symmetry in Lorentzian naturally reductive nilmanifolds.
method Analysis of 2-step nilpotent Lorentzian Lie groups with transitive isometry subgroups.
result Fixed points of isotropy representation indicate the distribution of symmetry.
We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model whose stationary distribution obeys detailed balance with respect to a parameteriz…
Transformers learn to generalize out-of-distribution with diverse pretraining tasks.
problem Conditions for pretrained transformers to generalize out-of-distribution.
method Empirical study of task diversity and pretraining distribution.
result As task diversity increases, transformers transition from specialized to generalized solutions.
Proposes a new model for time series that considers smooth transitions between states.
problem Models assume instantaneous transitions between discrete states, ignoring gradual changes.
method Dynamical Wasserstein Barycentric (DWB) model that estimates system state and pure state distributions over time.
result Accurately learns pure state distributions and improves state estimation for transition periods.
Continuous phase transitions identified in Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
problem Phase transitions in multimodal models and their properties.
method Sharp coercivity estimate and constrained Lebedev--Milin inequality.
result Continuous phase transitions at critical coupling strengths for Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
Study reveals phase transition in neural networks near interpolation.
problem Understanding generalization and learning transitions in neural networks.
method Effective theory for approximating Bayes-optimal generalisation error.
result Unveils a discontinuous phase transition between universal and specialisation phases.
Study measures investment funds' climate transition risk, finds moderate losses.
problem Measuring the impact of climate transition on investment portfolios.
method Comprehensive framework using geographical, sectoral, company and ISIN-level data.
result Investment funds suffer a moderate 5.7% loss in high transition risk scenario.
This paper resolves Breiman's dilemma in neural networks by analyzing phase transitions of margin dynamics.
problem Breiman's dilemma in neural networks: uniform margin improvement does not guarantee reduced generalization errors.
method Revisiting Breiman's dilemma in deep neural networks with spectrally normalized margins, analyzing phase transitions of normalized margin distributions.
result Margin-based generalization bounds can predict test error trends during training phase transitions.
Proposes MIVI for efficient posterior estimation and design of MCMC transitions.
problem Efficiently estimating posterior distributions in constrained time.
method Combines variational inference and MCMC with a variational distribution and optimized Markov chain.
result Optimized Markov chain improves variational distribution and vice versa, leading to more accurate posteriors.
Improved KSD test for better detection of differences in distributions.
problem Low power of KSD test when distributions have same modes but different mixing proportions.
method Perturb the observed sample using Markov transition kernels to improve KSD test power.
result Perturbed KSD test can lead to substantially higher power than the original KSD test.
A critical and challenging problem in reinforcement learning is how to learn the state-action value function from the experience replay buffer and simultaneously keep sample efficiency and faster convergence to a high quality solution. In prior works, transitions are uniformly sampled at random from the replay buffer o…
Study on eigenvalue distribution of correlated time series, showing deformation of Marchenko-Pastur distribution.
problem Eigenvalue distribution of Wishart matrix with temporal correlation.
method Analysis of moments and convergence to deformed Marchenko-Pastur distribution for Gaussian process with temporal correlation.
result Eigenvalue distribution converges to deformed Marchenko-Pastur distribution with longer tail and higher peak.
We study the problem of learning Markov decision processes with finite state and action spaces when the transition probability distributions and loss functions are chosen adversarially and are allowed to change with time. We introduce an algorithm whose regret with respect to any policy in a comparison class grows as t…
Modeling poverty transitions in India over 54 years, showing rising but persistent poverty.
problem Understanding and addressing poverty dynamics in India over long periods.
method Stochastic model of Geometric Brownian Motion with reallocation (RGBM).
result Annual poverty transitions are common, but poverty persists, especially among the poorest.
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gauss…
Adaptive populations such as those in financial markets and distributed control can be modeled by the Minority Game. We consider how their dynamics depends on the agents' initial preferences of strategies, when the agents use linear or quadratic payoff functions to evaluate their strategies. We find that the fluctuatio…
The hippocampal network approximates future locations using Nyström kernel approximations.
problem Learning neural representations for future locations under transition distributions.
method Formally derived neural network based on Nyström kernel approximations.
result The network successfully approximates transition distributions and yields sparse, localized receptive fields.
We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase …
Proposes a method to improve model-based reinforcement learning by matching multi-step rollout distributions.
problem Mismatching between model-based and real-world rollouts due to estimation error.
method Uses Wasserstein GAN (WGAN) to match the distributions of multi-step rollouts from the learned model to the real ones.
result The method minimizes the difference in cumulative rewards between the real and learned models.
Develops a new framework for conditional independence.
problem Generalizing previous notions of conditional independence.
method Introduces transition probability spaces and transitional random variables.
result Satisfies all desired relevance relations except symmetry.
We search for digital biomarkers from Parkinson's Disease by observing approximate repetitive patterns matching hypothesized step and stride periodic cycles. These observations were modeled as a cycle of hidden states with randomness allowing deviation from a canonical pattern of transitions and emissions, under the hy…
Proposes an alternative probabilistic interpretation of Huber loss.
problem Lack of intuitive understanding of Huber loss transition point.
method Relates Huber loss to Kullback-Leibler divergence between Laplace distributions.
result Identifies optimal transition point intuitively based on data noise.
New method improves robustness of deep learning with noisy labels.
problem Robust deep learning on corrupted labels with noisy samples.
method Meta-transition adaptation through clean meta data guidance.
result More accurate estimation of noise transition matrix and classifier parameters.
Deformation of semi-circle law for the correlated time series and Phase transitioncond-mat.stat-mech
Study on eigenvalue distribution of correlated time series deforming the semi-circle law.
problem Eigenvalue distribution of correlated time series differs from the semi-circle law.
method Analysis of Wigner random matrix with temporal correlation.
result Eigenvalue distribution converges to a deformed semi-circle law with longer tail and higher peak.
Model risk on credit riskq-fin.RM
This paper develops the Jungle model in a credit portfolio framework. The Jungle model is able to model credit contagion, produce doubly-peaked probability distributions for the total default loss and endogenously generate quasi phase transitions, potentially leading to systemic credit events which happen unexpectedly …
Violation of market efficiency in transition economiesphysics.soc-ph
We analyze the European transition economies and show that time series for most of major indices exhibit (i) power-law correlations in their values, power-law correlations in their magnitudes, and (iii) asymmetric probability distribution. We propose a stochastic model that can generate time series with all the previou…
Empirical Transfer Operators and Finite-Sample Change Detection for Noisy Expanding Interval Mapsstat.ML
Detect changes in noisy dynamical systems using empirical approximations and finite-sample bounds.
problem Change detection in noisy dynamical systems
method Partition-based empirical approximations and finite-state stationary distribution stability
result Finite-sample bound for empirical stationary density
This article considers a model for alternative processes for securities prices and compares this model with actual return data of several securities. The distributions of returns that appear in the model can be Gaussian as well as non-Gaussian; in particular they may have two peaks. We consider a discrete Markov chain …
Paper proposes an algorithm to estimate state aggregation from Markov transition data.
problem Estimating probabilistic aggregation map from system's trajectory.
method Two-step algorithm: spectral decomposition and linear transformation of singular vectors.
result Sharp error bounds for estimating aggregation and disaggregation distributions.
Framework optimizes transit routes based on crowd movements using demand prediction and supply optimization.
problem Dynamic optimization of transit routes in areas of crowd movements.
method Combines demand prediction (Quantile Regression) and supply optimization (Linear Programming) to dynamically redesign routes.
result Framework often obtains optimal solutions and outperforms conventional methods.
Several methods exist to infer causal networks from massive volumes of observational data. However, almost all existing methods require a considerable length of time series data to capture cause and effect relationships. In contrast, memory-less transition networks or Markov Chain data, which refers to one-step transit…
Recently, it was shown that there is a phase transition in the community detection problem. This transition was first computed using the cavity method, and has been proved rigorously in the case of groups. However, analytic calculations using the cavity method are challenging since they require us to understand p…
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
The paper studies phase transitions in Information Bottleneck for representation learning.
problem Understanding the behavior of compression and prediction terms in IB objective.
method Studied phase transitions in IB objective using second-order calculus of variations and Fisher information matrix.
result IB phase transitions correspond to learning new classes and are related to maximum correlation between input and target orthogonal to the learned representation.
Fractal Properties in Economicscond-mat.stat-mech
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition mechanism. By analyzing tick data of yen-dollar exchange rates we confirm two fractal pro…
RRPI improves offline RL by optimizing policies against worst-case dynamics.
problem Offline RL's performance degrades under distribution shift and transition uncertainty.
method Formulates offline RL as robust policy optimization, treating transition kernel as decision variable.
result RRPI achieves strong average performance on D4RL benchmarks, outperforming recent baselines.
QTD integrates quantization with diffusion for efficient data generation.
problem Challenges in continuous diffusion models, especially long-range transitions and biases.
method Quantized Transition Diffusion (QTD) integrates data quantization with discrete diffusion dynamics.
result QTD achieves efficient data generation with minimal score evaluations.
Estimates Markov chains from samples, solving two related prediction and estimation problems.
problem Estimating an unknown Markov chain from its samples.
method Considered two problems: predicting conditional distribution and estimating transition matrix, using KL-divergence and various -divergences.
result Resolved estimation problem for all sufficiently smooth -divergences, including KL-, , Chi-squared, Hellinger, and Alpha-divergences.
In this paper we study how to learn stochastic, multimodal transition dynamics in reinforcement learning (RL) tasks. We focus on evaluating transition function estimation, while we defer planning over this model to future work. Stochasticity is a fundamental property of many task environments. However, discriminative f…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to adapt their strategies together. This change in the environment results in dynamical…
On Transitive Consistency for Linear Invertible Transformations between Euclidean Coordinate Systemsmath.OC
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work addresses the problem of synchronizing transformations that are not transitively co…