Unified framework for efficient trans-dimensional Bayesian inference using VI and NFs.
problem Efficient trans-dimensional Bayesian inference with reduced computational cost.
method Variational inference with normalizing flows to train transport proposals.
result Our approach minimizes reverse KL divergence and reduces computational cost.
Improved KL divergence estimators for normalizing flows lead to faster convergence and better approximations.
problem Estimating KL divergences for normalizing flows efficiently and accurately.
method Path-gradient estimators for reverse and forward KL divergences.
result Path-gradient estimators lead to faster convergence and better approximation results.
Enhances RJMCMC efficiency with non-linear transport-based proposals.
problem Designing efficient RJMCMC proposals for complex models.
method Applies non-linear transport-based approach to construct efficient transdimensional jumps.
result Acceptance probability depends only on model probabilities when exact transports are used.
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
Classifies orientation-reversing homeomorphisms of even periods on surfaces.
problem Classifying orientation-reversing homeomorphisms of even periods on surfaces.
method Following the approach of [1] and correcting errors in [1] for the case of periods multiple of 4.
result Classification for orientation-reversing homeomorphisms of periods multiple of 4.
We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly reduced memory footprint, allowing them to scale to larger graphs. In the unsupervis…
DFM simplifies CNF training without interpolants.
problem Efficiently training CNFs with computationally expensive ODE solving.
method DFM optimizes dual vector fields for bijective transformations.
result DFM outperforms CNF trained with FM or ML objectives.
mfBm models and forecasts volatility with different Hurst exponents and correlations.
problem Modeling and forecasting volatility with varying Hurst exponents and correlations.
method Multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents, novel estimation method, time-reversibility test.
result mfBm reduces forecasting errors compared to a one-dimensional model and outperforms HAR model.
New method determines arrangement combinatorics from Milnor fiber boundary.
problem Determining arrangement combinatorics from Milnor fiber boundary.
method Explicit method using plumbing graph in normal form.
result Milnor fiber boundary determines arrangement combinatorics.
The paper proposes methods to extract and analyze individual variable information from complex dependencies.
problem Analyzing and understanding complex dependencies between multiple variables.
method Reversible normalization and iterative dependency reduction to extract individual information, and use it for direct mutual information and multi-feature Granger causality analysis.
result Decoupling of variables to analyze their individual information and direct mutual information transfers.
Method uses normalizing flows to efficiently sample from complex target densities.
problem Sampling from complex target densities with zero values in regions of transformation.
method Normalizing flows to address exploding reverse Kullback-Leibler divergence.
result Demonstrated efficient sampling from multi-mode complex density function.
DDS samples from noisy data by reversing diffusion, providing theoretical guarantees.
problem Sampling from unnormalized densities.
method Denoising diffusion process, score matching, optimal control, Schrödinger bridges.
result DDS provides theoretical guarantees for sampling.
Enhanced time series forecasting with improved trend and seasonal components.
problem Challenges in real-world time series forecasting, especially in multivariate applications.
method Individual decomposition of trend and seasonal components, using different approaches for each.
result Significant reduction in error values, around 10% MSE average reduction across benchmarks.
There are some statistical anomalies in the Chinese stock market, i.e., positive return skewness, anti-leverage effect (positive returns induce higher volatility than negative returns); and reverse volatility asymmetry (contemporaneous return-volatility correlation is positive). In this paper, we first confirm the exis…
A new model reconciles rough volatility and jumps.
problem Combining rough volatility and jump processes.
method Developed a reversionary Heston model with fast mean reversions and large vol-of-vols.
result The reversionary Heston model converges to Lévy jump processes for certain values of the parameter.
In 3D space forms, a lens minimizes volume for a fixed surface area.
problem Finding the shape with minimal volume for a given surface area in 3D space forms.
method Proving a sharp reverse isoperimetric inequality for λ-convex bodies. result The λ-convex lens minimizes volume for a fixed surface area in 3D space forms. Flow-based deep generative models learn data distributions by transforming a simple base distribution into a complex distribution via a set of invertible transformations. Due to the invertibility, such models can score unseen data samples by computing their exact likelihood under the learned distribution. This makes fl…
Spoken language translation (SLT) has become very important in an increasingly globalized world. Machine translation (MT) for automatic speech recognition (ASR) systems is a major challenge of great interest. This research investigates that automatic sentence segmentation of speech that is important for enriching speec…
PDDS samples from unnormalized densities using iterative particle scheme.
problem Sampling from unnormalized probability densities.
method Iterative particle scheme with novel score matching loss.
result Asymptotically consistent estimates for multimodal and high-dimensional tasks.
Entropy rigidity for Finsler flows but collapse for Reeb flows.
problem Entropy behavior of Reeb and Finsler flows on contact manifolds.
method Analysis of topological entropy for Reeb and Finsler flows.
result Uniform positive lower bound for Finsler flows but arbitrarily small topological entropy for Reeb flows.
SurVAE Flows combine VAEs and flows using surjective transformations.
problem Combining the strengths of VAEs and flows to model complex densities.
method Modular framework of composable deterministic and stochastic transformations.
result Exact likelihood computation and lower bound on likelihood.
A new method for reconstructing flows from perturbed distributions.
problem Reconstructing flows from perturbed probability distributions.
method Integrable vector fields and Green's functions.
result A nonparametric flow can be computed to generate samples from a perturbed distribution.
A new method uses MCMC-assisted normalizing flows for efficient Bayesian sampling.
problem Sampling from complex posterior distributions in Bayesian statistics.
method Training a normalizing flow using direct KL divergence and MCMC assistance.
result The method improves sampling efficiency for complicated posterior distributions.
SNPLA uses normalizing flows for efficient inference in implicit models.
problem Efficient inference in implicit models with complex likelihood and posterior learning.
method Sequential Neural Posterior and Likelihood Approximation (SNPLA) algorithm using normalizing flows.
result SNPLA achieves competitive performance with faster posterior draws compared to MCMC methods.
Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and automated reasoning. Computing the underlying structure and dynamics of such complex systems is extrem…
The paper proves reverse inequalities in various geometric settings using curvature radius data.
problem Proving reverse Alexandrov-Fenchel inequalities in different geometric settings.
method Using curvature radius data and associated evolute or focal maps.
result Sharp reverse Alexandrov-Fenchel estimates and inequalities in smooth convex curves and hypersurfaces.
New Fourier-based diffusion model improves high-frequency generation quality.
problem Diffusion models struggle with high-frequency details.
method Analyzed and modified the forward process in Fourier space to equalize noise corruption across frequencies.
result Improved generation quality for high-frequency components.
We propose a family of near-metrics based on local graph diffusion to capture similarity for a wide class of data sets. These quasi-metametrics, as their names suggest, dispense with one or two standard axioms of metric spaces, specifically distinguishability and symmetry, so that similarity between data points of arbi…
We consider the following problem: given two parallel and identically oriented bundles of light rays in n-dimensional Euclidean space and given a diffeomorphism between the rays of the former bundle and the rays of the latter one, is it possible to realize this diffeomorphism by means of several mirror reflections? We …
Classifies reversible and strongly reversible elements in quaternionic groups.
problem Classifying reversible and strongly reversible elements in quaternionic groups.
method Proves elements are reversible if and only if they are products of skew-involutions (resp. involutions).
result Proves elements are reversible if and only if they are products of skew-involutions (resp. involutions).
The paper classifies reversible and strongly reversible elements in Hermitian isometry groups.
problem Classifying reversible and strongly reversible elements in Hermitian isometry groups.
method Classification through group theory and algebraic manipulation.
result New classification of strongly reversible elements in Sp(n).
Matched filters reveal optimal normalization methods for different market participants.
problem Optimizing signal extraction from order flow for market microstructure analysis.
method General matched filter principle applied to normalization strategies.
result Optimal normalization methods (e.g., SMC and STV) differ based on trader types. We propose GraphNVP, the first invertible, normalizing flow-based molecular graph generation model. We decompose the generation of a graph into two steps: generation of (i) an adjacency tensor and (ii) node attributes. This decomposition yields the exact likelihood maximization on graph-structured data, combined with t…
A new perspective on self-attention models using MLPs.
problem Improving sequence modeling with self-attention mechanisms.
method Introducing HyperMLP and HyperGLU, which use dynamic two-layer MLPs with reverse-offset layout.
result HyperMLP/HyperGLU consistently outperform softmax-attention baselines.
This paper classifies reversible and strongly reversible elements in affine groups.
problem Classifying reversible and strongly reversible elements in affine groups.
method Identifying affine transformations and using conjugacy by involutions.
result Classification of reversible and strongly reversible elements in affine groups.
We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in R3. In particular, we give obstructions to a concordance from an arbitrary knot to the standard Legendrian unknot, in terms of normal rulings. We also place strong restrictions on knots that have concord…
New neural net learns time-reversible symplectic dynamics.
problem Lack of time-reversibility in neural networks for symplectic systems.
method Proposes a new neural network architecture for time-reversible symplectic systems.
result Demonstrates learning of time-reversible symplectic dynamics from data.
A new trading strategy using reinforcement learning for statistical arbitrage.
problem Traditional statistical arbitrage models rely on model assumptions and price deviations from a long-term mean.
method Empirical reversion time metric, reinforcement learning framework, and state space optimization.
result Optimal mean reversion strategy identified through reinforcement learning.
Improved generalization with semantic perturbations using normalizing flows.
problem Overfitting in deep neural networks training.
method Use normalizing flows for generating semantically meaningful perturbations in latent space.
result Achieved 96.6% test accuracy on CIFAR-10 with ResNet-18, outperforming existing methods.
Algebraic method reveals criterion for quaternionic Möbius group reversibility.
problem Characterizing reversibility in quaternionic Möbius group elements.
method Purely algebraic approach using matrix entries and conjugacy invariants.
result Explicit criterion for reversibility in terms of matrix entries.
Recent studies have shown that online portfolio selection strategies that exploit the mean reversion property can achieve excess return from equity markets. This paper empirically investigates the performance of state-of-the-art mean reversion strategies on real market data. The aims of the study are twofold. The first…
A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodes…
Sharp stability results for reverse isoperimetric inequalities in 2D.
problem Reverse isoperimetric inequalities in the plane.
method Stability analysis of λ-convex bodies and convex bodies with smooth boundaries. result Sharp stability results for reverse isoperimetric inequalities, including inradius and Cheeger inequalities.
Let G be a group. An element g in G is called reversible if it is conjugate to g−1 within G, and called strongly reversible if it is conjugate to its inverse by an order two element of G. Let HHn be the n-dimensional quaternionic hyperbolic space. Let PSp(n,1) be the i…
A new method improves posterior approximation for complex distributions.
problem Difficulty in capturing multimodal and heavy-tailed posteriors with standard normalizing flows.
method StiCTAF: stick-breaking mixture base with component-wise tail adaptation.
result Improved tail recovery and better mode coverage compared to benchmarks.
Boundary rigidity proven for non-reversible Finsler metrics.
problem Recovering non-reversible Finsler metrics from boundary distance data.
method Sum of reversible Finsler norm and closed 1-form, boundary rigidity results.
result 1-form can be uniquely recovered from boundary distance data.
On-line portfolio selection has attracted increasing interests in machine learning and AI communities recently. Empirical evidences show that stock's high and low prices are temporary and stock price relatives are likely to follow the mean reversion phenomenon. While the existing mean reversion strategies are shown to …
Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.
problem Approximating target distributions in conditional diffusion models.
method Using finite Gaussian mixtures with ReLU-network logits as reverse kernels, reducing the problem to static conditional density approximation.
result The resulting neural reverse-kernel class is dense in conditional KL divergence under exact terminal matching.