arXiv research

We propose a neural superstatistics method to estimate dynamic cognitive models from time series data.

Share price returns on different time scales can be well modelled by a superstatistical dynamics. Here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales. It is shown that while chi-square superstatistics works well on a time scale…

We report a general technique to study a given experimental time series with superstatistics. Crucial for the applicability of the superstatistics concept is the existence of a parameter $β$ that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration. The propose…

Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data. Here we show tha…

Bayesian inference and superstatistics model financial volatility dynamics across different timescales.

Financial time series have been investigated to follow fat-tailed distributions. Further, an empirical probability distribution sometimes shows cut-off shapes on its tails. To describe this stylized fact, we incorporate the cut-off effect in superstatistics. Then we confirm that the presented stochastic model is capabl…

We discuss superstatistics theory of labour productivity. Productivity distribution across workers, firms and industrial sectors are studied empirically and found to obey power-distributions, in sharp contrast to the equilibrium theories of mainstream economics. The Pareto index is found to decrease with the level of a…

Labour productivity distribution (dispersion) is studied both theoretically and empirically. Superstatistics is presented as a natural theoretical framework for productivity. The demand index $κ$ is proposed within this framework as a new business index. Japanese productivity data covering small-to-medium to large firm…

We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive "superstatistics" that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde)that exhibit transitio…

Study characterizes learning from heavy-tailed data in high dimensions using superstatistical methods.

We consider an ideal closed stock market, in which 100 traders have economic activities. The assets of the traders change through buying and selling stocks. We simulate the assets under conservation of both total currency and total number of stocks. If the traders are identical, then the assets are distributed as a sta…

The study analyzes river water quality using statistical and machine learning methods.

Osborne's paradox explained via Bayesian inference and superstatistics.

This work models financial market returns with asymmetric Tsallis distributions, improving fit over symmetric q-Gaussians.

We study productivity dispersions across workers, firms and industrial sectors. Empirical study of the Japanese data shows that they all obey the Pareto law, and also that the Pareto index decreases with the level of aggregation. In order to explain these two stylized facts, we propose a theoretical framework built upo…

We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or sup…

Study on price fluctuations and persistence in European electricity spot markets.

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the …

Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active per…

Graphs of neural networks are represented to preserve symmetry, improving performance across various tasks.

Convolutional Neural Processes improve data efficiency in neural processes.

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous ne…

Investigates how neural network graph structure impacts predictive performance.

Neural Tangents simplifies infinite-width neural networks for research.

Novel framework explains generalization in deep neural networks.

Neural networks can approximate functions uniformly across various measures.

Investigates neural codes and their embeddings, proving conjectures and introducing new code types.

Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we present a compact neural circuit for two common numerical integrators: the explicit …

Quadratic models explain neural network behavior during training.

Graph Metanetworks process diverse neural architectures efficiently.

Optimal rates for shallow ReLU networks in nonparametric regression.

New metric compares noisy neural trajectories using optimal transport.

Paper analyzes Q-learning with neural networks, proving a fast convergence rate.

The neural tangent kernel equivalence theorem fails in practice.

Equivariant neural networks use symmetry to interpret complex data.

Two new criteria help understand the advantage of deep neural networks.

Use simplified layerwise linear models to understand neural dynamics.

Analysis of over-parameterized neural networks has drawn significant attention in recentyears. It was shown that such systems behave like convex systems under various restrictedsettings, such as for two-level neural networks, and when learning is only restricted locally inthe so-called neural tangent kernel space aroun…

The paper proves consistency of neural networks with regularization.

This study shows why training Neural ODEs is hard and proposes a new method.

We introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of sparsely observed context points as input, and outputs a distribution over targ…

Paper benchmarks quantum neural networks against classical ones for binary classification tasks.

Affine spiking neural networks learn efficiently and generalize well.

Explains equivariant neural networks for machine learning.

Bayesian Neural Networks improve uncertainty estimation in deep learning.

Proposes deep graph persistence to address neural persistence issues in deep learning.

Study of infinitely deep but narrow neural networks using NTK theory.

Paper introduces a noise-robust classification method using hypergraph neural networks.