Contrastive Divergence (CD) and Persistent Contrastive Divergence (PCD) are popular methods for training the weights of Restricted Boltzmann Machines. However, both methods use an approximate method for sampling from the model distribution. As a side effect, these approximations yield significantly different biases and…
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48 results for “Persistent Contrastive Divergence”
Continuous-time PCD for MLE with explicit error bounds.
problem Maximum likelihood estimation of unnormalised densities.
method Continuous-time formulation as coupled SDEs, deriving UiT bounds.
result Explicit error bounds between PCD iterates and MLE solution.
Learning algorithms for energy based Boltzmann architectures that rely on gradient descent are in general computationally prohibitive, typically due to the exponential number of terms involved in computing the partition function. In this way one has to resort to approximation schemes for the evaluation of the gradient.…
New method tackles incomplete data in RBM inverse Ising problems.
problem Computing data and model expectations in inverse Ising problems with missing observations.
method Combines mean-field approximation, persistent contrastive divergence, and spatial Monte Carlo integration.
result Effective and accurate tuning of model parameters compared to conventional methods.
Persistently trained EBMs generate images and estimate complex densities.
problem Challenges in ML learning for energy-based models, especially non-convergence of MCMC.
method Introduce diffusion data, learn a joint EBM through persistent training with enhanced sampling.
result First simultaneous achievement of stability, post-training image generation, and superior out-of-distribution detection for image data.
Generalizes SMCI to improve Boltzmann machine learning accuracy.
problem Limitation in applying higher-order SMCI to dense systems.
method Generalized SMCI (GSMCI) and new PBM learning method.
result GSMCI allows higher-order approximations for dense systems.
Restricted Boltzmann machines are undirected neural networks which have been shown to be effective in many applications, including serving as initializations for training deep multi-layer neural networks. One of the main reasons for their success is the existence of efficient and practical stochastic algorithms, such a…
CRBMs improve financial regime detection with PCD and free energy analysis.
problem Detecting systemic risk regimes in financial time series.
method Extended RBM to CRBM with autoregressive conditioning and PCD. Decomposed free energy into magnitude and correlation components.
result CRBM's free energy metric distinguishes between magnitude shocks and market regimes.
RényiCL uses Rényi divergence for robust contrastive learning with stronger data augmentations.
problem Learning useful representations from multiple data views with hard augmentations.
method RényiCL employs Rényi divergence for contrastive learning, using a novel variational objective to manage hard negative sampling.
result RényiCL achieves better performance with stronger augmentations compared to other methods.
This paper studies the problem of parameter learning in probabilistic graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps. However, both E and M steps are computationally intractable for high dimensional d…
Quantum annealing (QA) is a hardware-based heuristic optimization and sampling method applicable to discrete undirected graphical models. While similar to simulated annealing, QA relies on quantum, rather than thermal, effects to explore complex search spaces. For many classes of problems, QA is known to offer computat…
Conservative objective models are a special kind of contrastive divergence-based energy modelstat.ML
Theoretical proof shows COMs are a type of contrastive divergence model with improved sampling.
problem Improving sampling quality in offline model-based optimization.
method Showed COMs are contrastive divergence models, proposed Langevin MCMC sampler, and decoupled model.
result Improved sampling quality achieved by decoupling model and using Langevin MCMC.
NCE and CD are shown to be equivalent ML methods.
problem Estimating unnormalised models without normalisation constant.
method NCE uses proxy criterion, CD uses importance sampling.
result NCE and CD are equivalent ML methods.
Paper proposes f-EBM for training deep EBMs using various f-divergences.
problem Training deep EBMs with intractable partition functions.
method Introduces f-EBM framework and optimization algorithm for any f-divergence.
result f-EBM outperforms contrastive divergence and other f-divergences.
This paper proposes a more efficient training method for energy-based models.
problem The computational burden and validity trade-off in Contrastive Divergence training.
method Introducing Diffusion Contrastive Divergence (DCD) to replace Langevin dynamics with diffusion processes.
result The proposed DCDs are more computationally efficient and handle gradient terms better than Contrastive Divergence.
The Data Clustering (DC) problem is of central importance for the area of Machine Learning (ML), given its usefulness to represent data structural similarities from input spaces. Differently from Supervised Machine Learning (SML), which relies on the theoretical frameworks of the Statistical Learning Theory (SLT) and t…
CD algorithm achieves near-optimal convergence rate for unnormalized models.
problem Training unnormalized models with high efficiency.
method Non-asymptotic analysis of contrastive divergence algorithm.
result CD can achieve convergence rate under regularity assumptions.
We develop a method to combine Markov chain Monte Carlo (MCMC) and variational inference (VI), leveraging the advantages of both inference approaches. Specifically, we improve the variational distribution by running a few MCMC steps. To make inference tractable, we introduce the variational contrastive divergence (VCD)…
The study reveals distinct patterns in retail investors' holding periods affecting stock returns.
problem Understanding the impact of retail investors' investment horizons on stock returns.
method Using self-reported holding periods from StockTwits, the study categorizes retail investors into long-horizon and short-horizon groups and analyzes their return patterns.
result Long-horizon retail investors exhibit underreaction to earnings announcements, while short-horizon investors show overreaction.
New statistical theory explains contrastive learning effectiveness.
problem Understanding why contrastive learning works well for representation extraction.
method Developed a new theoretical framework based on approximate sufficient statistics.
result Near-sufficient encoders derived from contrastive learning can be adapted for downstream tasks.
This paper proposes a multi-grid method for learning energy-based generative ConvNet models of images. For each grid, we learn an energy-based probabilistic model where the energy function is defined by a bottom-up convolutional neural network (ConvNet or CNN). Learning such a model requires generating synthesized exam…
Simplicial persistence of financial markets: filtering, generative processes and portfolio riskq-fin.ST
Simplicial persistence measures financial market dynamics, revealing long-term structure evolution.
problem Understanding the long-term structure evolution of financial markets.
method Simplicial persistence, null models, TMFG filtering, thresholding, generative process analysis.
result More liquid markets exhibit slower persistence decay, suggesting higher fragility to systemic shocks.
VCL adds uncertainty to contrastive learning models.
problem Lack of uncertainty quantification in contrastive learning methods.
method VCL uses a decoder-free framework that maximizes ELBO with InfoNCE loss and KL divergence.
result VCL provides meaningful uncertainty estimates and matches deterministic baselines in accuracy.
The paper explores how Finsler manifolds differ from Riemannian ones in functional inequalities.
problem Analytic phenomena on Finsler manifolds differ from Riemannian ones.
method Comparative analysis of Finsler and Riemannian manifolds.
result Functional inequalities (Hardy, uncertainty, CKN) behave differently on Finsler manifolds.
Paper proposes f-DPG for aligning language models with preferences.
problem Aligning language models with user preferences.
method Uses f-divergence to approximate target distributions and minimizes a forward KL from it using DPG.
result Jensen-Shannon divergence often outperforms forward KL divergence, leading to significant improvements.
Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19q-fin.ST
Study shows similarities and differences in crypto and equity dynamics during pandemic.
problem Comparing cryptocurrency and equity market dynamics during the pandemic.
method New methodologies applied to study cryptocurrency and equity market dynamics, including recently introduced methods for trajectory and anomaly analysis.
result Cryptocurrencies exhibit stronger collective dynamics and correlation, while equities show greater persistence in anomalies over time.
The paper explores how Finsler manifolds differ from Riemannian ones in functional inequalities.
problem Analytic phenomena on Finsler manifolds differ from Riemannian ones.
method Comparative analysis of Finsler and Riemannian manifolds, focusing on Sobolev spaces, Hardy inequalities, and uncertainty principles.
result Functional inequalities (Hardy, uncertainty) break down on Finsler Cartan-Hadamard manifolds, while Caffarelli-Kohn-Nirenberg inequality exhibits a sharp threshold.
Central to robot exploration and mapping is the task of persistent localization in environmental fields characterized by spatially correlated measurements. This paper presents a Gaussian process localization (GP-Localize) algorithm that, in contrast to existing works, can exploit the spatially correlated field measurem…
Self-supervised and supervised methods learn similar intermediate visual representations but diverge in final layers.
problem Comparing self-supervised and supervised methods for visual learning.
method Comparison of contrastive self-supervised and supervised methods on simple image data.
result Contrastive and supervised methods learn similar intermediate representations but diverge in final layers.
New theory explains GAN's high quality but low diversity.
problem Lack of theoretical justification for non-saturating GAN training.
method Showed non-saturating GAN training approximately minimizes a specific f-divergence.
result Non-saturating GAN training minimizes a particular f-divergence.
Paper proves large deviation principle for stochastic approximations.
problem Asymptotic estimates of learning algorithm deviations.
method Weak convergence approach to large deviations.
result Identifies appropriate scaling sequence and new representation for rate function.
This study uses persistent homology to analyze complex transitional networks from time series data.
problem Lack of effective tools to summarize complex topology in transitional networks.
method Persistent homology from topological data analysis applied to coarse-grained state-space networks (CGSSN).
result CGSSN improves dynamic state detection and noise robustness compared to other methods.
Disagreement between two classifiers regarding the class membership of an observation in pattern recognition can be indicative of an anomaly and its nuance. As in general classifiers base their decision on class aposteriori probabilities, the most natural approach to detecting classifier incongruence is to use divergen…
Study forecasts U.S. bond index using deep learning, finding persistence is key.
problem Forecasting U.S. aggregate bond index with deep learning methods.
method Constructed a stationary but maximally persistent representation of the bond index, evaluated using MLPs and CNNs.
result Deep learning models outperform traditional methods in short-horizon forecasting of bond indices.
Contrastive divergence (CD) is a promising method of inference in high dimensional distributions with intractable normalizing constants, however, the theoretical foundations justifying its use are somewhat shaky. This document proposes a framework for understanding CD inference, how/when it works, and provides multiple…
Estimating the log-likelihood gradient with respect to the parameters of a Restricted Boltzmann Machine (RBM) typically requires sampling using Markov Chain Monte Carlo (MCMC) techniques. To save computation time, the Markov chains are only run for a small number of steps, which leads to a biased estimate. This bias ca…
New measure EC assesses node contributions in nonlinear, time-varying systems.
problem Existing node contribution measures assume linear, time-invariant dynamics, failing for complex, real-world systems.
method Defined 'emergent contribution (EC)' as a dynamical leverage measure from Jacobians of differentiable models.
result EC diverges from average controllability under persistent regime switching and sign reversal, identifying limits of local linearization.
Divergence Triangle for Joint Training of Generator Model, Energy-based Model, and Inference Modelstat.ML
This paper proposes the divergence triangle as a framework for joint training of generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly integrates variational learning, adversarial learning, wake-sleep algorithm, an…
SGDm with fixed step-size diverges under covariate shift, similar to a parametric oscillator.
problem SGDm with fixed step-size diverges under covariate shift.
method Approximated learning system as a time-varying system of ODEs and characterized divergence/convergence modes.
result SGDm with fixed step-size can diverge under covariate shift, similar to resonance in oscillators.
Parametric adversarial divergences, which are a generalization of the losses used to train generative adversarial networks (GANs), have often been described as being approximations of their nonparametric counterparts, such as the Jensen-Shannon divergence, which can be derived under the so-called optimal discriminator …
Distinguishing between classes of time series sampled from dynamic systems is a common challenge in systems and control engineering, for example in the context of health monitoring, fault detection, and quality control. The challenge is increased when no underlying model of a system is known, measurement noise is prese…
Fisher Auto-Encodersstat.ML
Fisher auto-encoders use Fisher divergence for more robust generative modeling.
problem Model uncertainty in generative models.
method Minimizing Fisher divergence between true and modeled joint distributions.
result Fisher auto-encoders can more accurately quantify model uncertainty.
Co-TSFA improves time series forecasting by distinguishing between short-lived and persistent anomalies.
problem Standard forecasting models fail to distinguish between short-lived and persistent anomalies, leading to overreaction or underreaction.
method Co-TSFA learns to ignore forecast-irrelevant anomalies and respond to forecast-relevant ones through input-only and input-output augmentations and a latent-output alignment loss.
result Co-TSFA improves performance under anomalous conditions while maintaining accuracy on normal data.
By exploiting the property that the RBM log-likelihood function is the difference of convex functions, we formulate a stochastic variant of the difference of convex functions (DC) programming to minimize the negative log-likelihood. Interestingly, the traditional contrastive divergence algorithm is a special case of th…
Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as both the nominal and anomalous multivariate data distributions are assumed unkno…
CD learning is shown to be an adversarial game for fitting models.
problem Difficulty in understanding the convergence properties of CD learning.
method Presented an alternative derivation of CD without approximation, showing it as a time-reversal adversarial game.
result CD is an adversarial learning procedure where a discriminator tries to classify time-reversed Markov chains.
We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent estimation methods such as noise-contrastive estimation, ratio matching, and sco…
The natural gradient of ELBO vanishes in unconstrained optimization, simplifying learning.
problem The gap between evidence and ELBO has a vanishing natural gradient.
method Analyzes the Fisher-Rao gradient of ELBO and its implications for learning.
result Maximizing ELBO is equivalent to minimizing KL divergence, simplifying learning.