A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper introduces a method to estimate log-likelihood in VAE models.
The log-determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often intractable when the size of the kernel matrix exceeds a few t…
This work gives an in-depth derivation of the trainable evidence lower bound obtained from the marginal joint log-Likelihood with the goal of training a Multi-Modal Variational Autoencoder (MVAE).
The presence of log-periodic structures before and after stock market crashes is considered to be an imprint of an intrinsic discrete scale invariance (DSI) in this complex system. The fractal framework of the theory leaves open the possibility of observing self-similar log-periodic structures at different time scales.…
Two sets of high quality income data are analysed in detail, one set from the UK, one from the USA. It is firstly demonstrated that both a log-normal distribution and a Boltzmann distribution can give very accurate fits to both these data sets. The absence of a power tail in the US data set is then discussed. Taken in …
New method corrects Laplace/BIC errors in singular models, revealing effective dimension.
Develops an anytime-valid framework for optimal policy identification from logged contextual bandit data.
Stochastic Bayesian Neural Network improves scalability and performance.
Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present theoretical and empirical evidence that over-parameterization can help EM avoid …
Bitcoin volatility shows multifractal structure, contradicting rough volatility models.
This work improves VAEs using MCMC methods for better variational bounds.
Fractal analysis is carried out on the stock market indices of seven European countries and the US. We find evidence of long range dependence in the log return series of the Mibtel (Italy) and the PX Glob (Czech Republic). Long range dependence implies that predictable patterns in the log returns do not dissipate quick…
Proposes a deep neural network for event intensity estimation.
ECLIPSE detects AI hallucinations in finance with high accuracy.
Stochastic variational inference (SVI) plays a key role in Bayesian deep learning. Recently various divergences have been proposed to design the surrogate loss for variational inference. We present a simple upper bound of the evidence as the surrogate loss. This evidence upper bound (EUBO) equals to the log marginal li…
Diffusion models adapt to data geometry through log-domain smoothing.
Since August 2000, the stock market in the USA as well as most other western markets have depreciated almost in synchrony according to complex patterns of drops and local rebounds. In \cite{SZ02QF}, we have proposed to describe this phenomenon using the concept of a log-periodic power law (LPPL) antibubble, characteriz…
Develops a support-aware framework for reserve-policy selection in advertising markets.
Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently pro…
Bayesian inference and superstatistics model financial volatility dynamics across different timescales.
In this paper we review the concepts of Bayesian evidence and Bayes factors, also known as log odds ratios, and their application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical techniques. Specific attention is paid to the Laplace approximation, variational Ba…
We study dynamical behavior of the Chinese stock markets by investigating the statistical properties of daily ensemble returns and varieties defined respectively as the mean and the standard deviation of the ensemble daily price returns of a portfolio of stocks traded in China's stock markets on a given day. The distri…
We apply two non-parametric methods to test further the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The analysis using the so-called (H,q)-derivative is applied to seven time series ending with the October 1987…
The CAP slope is Bayes' theorem in cumulative coordinates, unlocking the weight of evidence, Somers' D, and Gini coefficient.
Transformers for binary decisions are sensitive to evidence order, leading to unreliable outcomes.
A hypothesis that the financial log-periodicity, cascading self-similarity through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly well using a single and unique value of the preferred scaling factor lambda=2, whi…
We study the scalar curvature of Kähler metrics that have cone singularities along a divisor, with a particular focus on certain specific classes of such metrics that enjoy some curvature estimates. Our main result is that, on the projective completion of a pluricanonical bundle over a product of Kähler--Einstein Fano …
We argue that the word ``critical'' in the title is not purely literary. Based on our and other previous work on nonlinear complex dynamical systems, we summarize present evidence, on the Oct. 1929, Oct. 1987, Oct. 1987 Hong-Kong, Aug. 1998 global market events and on the 1985 Forex event, for the hypothesis advanced f…
The study examines volatility models and finds decoupling of short- and long-term correlation structures.
The Links-Gould invariant of alternating links has log-concave coefficients.
Following our previous investigation of the USA Standard and Poor index anti-bubble that started in August 2000, we analyze thirty eight world stock market indices and identify 21 anti-bubble. An ``anti-bubble'' is defined as a self-fulfilling decreasing price created by positive price-to-price feedbacks feeding overal…
DLM for BNNs fails to improve over ELBO optimization.
Paper analyzes IHT's performance in sparse recovery problems.
Normalizing flow regression approximates posterior distributions without additional sampling.
We clarify the status of log-periodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum's [2001] criticism and show how it can be rebuked. Feigenbaum's main result is as follows: ``the hypothesis that the log-periodic component is present in the data cannot be reje…
Improved cutting plane method for convex optimization and games.
Dropout-based regularization methods can be regarded as injecting random noise with pre-defined magnitude to different parts of the neural network during training. It was recently shown that Bayesian dropout procedure not only improves generalization but also leads to extremely sparse neural architectures by automatica…
New score helps choose PIML model parameters, reducing ambiguity in model quality.
VAEs improve representation learning by inverting the data-generating process through self-consistency.
Unified Bayesian model explains in-context learning and activation steering in LLMs.
New algorithm samples neural network posteriors efficiently.
Corrected graph convolutions improve node classification on graphs.
Introduces log S-fBM model to unify rough and multifractal volatility.
In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using cross-validation on held-out data, either through -fold partitioning or leave-$p…
Non-negative matrix factorization (NMF) is a knowledge discovery method that is used in many fields. Variational inference and Gibbs sampling methods for it are also wellknown. However, the variational approximation error has not been clarified yet, because NMF is not statistically regular and the prior distribution us…
New bounds on SGD's final iterate convergence rate in constant dimension.
Online method for state estimation and parameter learning in SSMs.
The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from s…