ACP-UCB1 ranks arms based on upper-tail performance, improving stochastic bandit algorithms.
problem Stochastic bandit algorithms often favor arms with strong upper-tail performance, which is not well-addressed by classical mean-reward criteria.
method ACP-UCB1 combines an adaptive conformal estimate of the upper endpoint with a UCB-type optimism bonus.
result ACP-UCB1 achieves logarithmic upper-quantile regret with per-arm contribution \(O(
icefrac{\log n}{Δ_j^{\mathrm{ACP}}})\).
The univariate piecing-together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. We propose a multivariate extension. First it is shown that an arbitrary copula is in the domain of attraction of a multivariate extreme value …
New method optimizes language model performance for test-time strategies.
problem Mismatch between training objectives and test-time deployment of large language models.
method Tail-Extrapolated estimators to approximate best-of-N performance from limited training rollouts.
result Improved performance of best-of-N deployment across various models and datasets.
This study examines biases in flow matching samplers using finite-sample estimation.
problem Biases in flow matching samplers when using finite-sample surrogates.
method Finite-sample plug-in estimation and hierarchy of empirical FM models.
result Exact empirical minimizer and smoothed plug-in regime identified for affine conditional flows.
Proposes QGC to distinguish between lower and upper tail connectivity in financial networks.
problem Identifying systemically important firms using financial data.
method Quantile Granger Causality (QGC) using Lasso penalized quantile regressions.
result QGC networks detect systemic risk more accurately than mean-based networks.
Study growth patterns in random networks using i.i.d. perturbations.
problem Understanding the growth of affine regions in random piecewise-linear networks.
method Analyzes a random compositional model with i.i.d. perturbations of the tent map, proving submultiplicative pressure and using finite-state defect process for upper-tail lower bounds.
result Proves the existence of a submultiplicative pressure for \(N_n\) and gives exponential upper bounds for \(n^{-1}\log N_n\).
Proposes a copula-based filter for diabetes risk prediction.
problem Feature selection for robust and interpretable predictive modeling in medicine, especially for extreme patient strata.
method Copula-based supervised filter using Gumbel-copula implied upper-tail concordance score (lambda U).
result The proposed filter outperforms standard filters and provides clinically coherent predictors.
Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is ``interrupted'' by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the distribution contrasts with a lar…
Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be highly variable when the importance ratios have a heavy right tail. This routinely occurs when there are aspects of the target distribution that are not well captur…
Financial markets can be seen as complex systems that are constantly evolving and sensitive to external disturbance, such as systemic risks and economic instabilities. Analysis of resilient market performance, therefore, becomes useful for investors. From a systems perspective, this paper proposes a novel function-base…
Graphs with non-negative Ollivier-Ricci curvature cannot be expanders.
problem Understanding the relationship between graph curvature and expansion properties.
method Proving an inequality linking isoperimetric profiles to total variation decay of random walks.
result Graphs with non-negative Ollivier-Ricci curvature cannot be expanders.
Estimates change points in Weibull time series with copulas.
problem Change-point estimation for nonlinear Weibull time series with copula-based Markov models.
method Copula-based Markov chain model with Weibull marginal distributions, incorporating asymmetric dependence structures through Clayton and Joe copulas.
result Proposed method performs well in estimating change points and model parameters, demonstrated through extensive numerical studies and empirical application.
Although deep learning has been applied to successfully address many data mining problems, relatively limited work has been done on deep learning for anomaly detection. Existing deep anomaly detection methods, which focus on learning new feature representations to enable downstream anomaly detection methods, perform in…
In this paper we address the question of the size distribution of firms. To this aim, we use the Bloomberg database comprising multinational firms within the years 1995-2003, and analyze the data of the sales and the total assets of the separate financial statement of the Japanese and the US companies, and make a compa…
Interpolating models can have heavy-tailed risk, leading to rare but severe errors.
problem Interpolating models' tail risk is poorly understood, affecting rare but impactful errors.
method Large-deviation methods to study the fragility of high-dimensional linear interpolators.
result Ridgeless regression exhibits heavy-tailed risk, while ridge-regularized estimators have better tail behavior.
We use data on wealth of the richest persons taken from the "rich lists" provided by business magazines like Forbes to verify if upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover the world's richest persons over 1996-2012, the richest Americans over 1988-2012,…
We investigate the shape of the Italian personal income distribution using microdata from the Survey on Household Income and Wealth, made publicly available by the Bank of Italy for the years 1977--2002. We find that the upper tail of the distribution is consistent with a Pareto-power law type distribution, while the r…
By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find t…
Proposes a method to improve pWCET estimation for heavy-tailed distributions.
problem Improving pWCET estimation for heavy-tailed distributions in real-time systems.
method Incorporates saturating functions into Chebyshev's inequality to mitigate the influence of large outliers.
result Achieves safe and tighter bounds for heavy-tailed distributions.
Unified framework for critical scaling of inverse temperature in self-attention.
problem Conflicting inverse-temperature laws for long-context self-attention.
method Counting gaps and defining an upper-tail accumulation scale.
result Critical inverse-temperature scale determined by gap-counting function.
Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the investigated variables. A non-equilibrium difference of money temperatures betw…
A bipartite producer-consumer network is constructed to describe the industrial structure. The edges from consumer to producer represent the choices of the consumer for the final products and the degree of producer can represent its market share. So the size distribution of firms can be characterized by producer's degr…
This study examines local co-movements in energy, agriculture, and metal markets using copulas.
problem Identifying local dependencies and asymmetries in energy, agriculture, and metal markets.
method Non-parametric mixture copula and copula-based local Kendall's tau approach.
result Increased co-movements in extreme situations, asymmetric local dependence, and diversification potential.
Many studies in Economics and other disciplines have been reporting distributions following power-law behavior (i.e distributions of incomes (Pareto's law), city sizes (Zipf's law), frequencies of words in long sequences of text etc.)[1, 6, 7]. This widespread observed regularity has been explained in many ways: genera…
In this paper, we quantitatively investigate the properties of a statistical ensemble of stock prices. We focus attention on the relative price defined as X(t)=S(t)/S(0), where S(0) is the initial price. We selected approximately 3200 stocks traded on the Japanese Stock Exchange and formed a statistical ensem…
This Chapter is written for the Festschrift celebrating the 70th birthday of the distinguished economist Duncan Foley from the New School for Social Research in New York. This Chapter reviews applications of statistical physics methods, such as the principle of entropy maximization, to the probability distributions of …
Quantum method speeds up risk estimation for insurance tail risks.
problem Sample-sparsity in classical Monte Carlo methods for tail risk pricing.
method Quantum Amplitude Estimation (QAE) with Grover amplification.
result Quantum method achieves convergence approaching order reciprocal N, enabling high-resolution tail estimation within practical budgets.
New method recalibrates VaR for option books, reducing forecast errors.
problem Inaccurate VaR forecasts due to missing operational choices.
method Marking-aware sequential VaR recalibration targeting normalized book-level loss.
result Sequential VaR recalibration improves VaR performance across different markets and options.
Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any type of dependency structure given sufficient sample size. One major bottleneck is…
We present new excess risk bounds for general unbounded loss functions including log loss and squared loss, where the distribution of the losses may be heavy-tailed. The bounds hold for general estimators, but they are optimized when applied to η-generalized Bayesian, MDL, and empirical risk minimization estimators. …
Study of Polymarket's prediction market microstructure using tick-level order book data.
problem Understanding the microstructure of decentralized prediction markets.
method Analysis of a continuous tick-level order book feed and on-chain trade records.
result Trade direction inferred from Polymarket's public order-book feed disagrees with on-chain data in ~59% of cases.
A new tail-shape index based on Value at Risk and Expected Shortfall.
problem Measuring and comparing tail behavior of loss distributions.
method Introducing a new θ-index based on equal level relationships between Value at Risk and Expected Shortfall. result The θ-index provides a level-dependent, scale-free measure of upper tail behavior. Investors optimize their portfolios within a Wasserstein ball to match a benchmark's risk profile.
problem Optimizing portfolio performance while maintaining risk proximity to a benchmark.
method Optimal dynamic strategy selection based on minimizing distortion risk measures within a Wasserstein ball.
result An optimal dynamic strategy exists and can be calculated through isotonic projections.
Cryptocurrency markets exhibit violent, synchronised drawdowns, challenging diversification claims.
problem Cryptocurrency markets' violent drawdowns challenge diversification claims.
method Dynamic conditional tail dependence analysis
result Near-complete and stable lower-tail graph, upper tail that thins over time, dissolution of token categories into a core.
Deep models predict intraday electricity prices accurately.
problem Accurately forecasting intraday electricity prices.
method Two deep time series probabilistic models using ESNs with stochastic disturbances and copulas.
result Deep distributional models provide accurate short-term probabilistic price forecasts.
Modified lognormal distribution with flexible tails for skewed data.
problem Skewed and fat-tailed data in natural and engineering datasets.
method Developed a family of three-parameter non-Gaussian probability density functions based on generalized kappa-exponential and kappa-logarithm functions.
result Closed-form analytic expressions for statistical functions and maximum-likelihood estimation.
Geometric framework for signed multivariate tail-dependence compatibility at various thresholds.
problem Modeling and analyzing signed multivariate tail-dependence across different thresholds.
method Developed a geometric witness framework to represent and invert signed tail families, identifying nonnegative weights and normalized masses.
result Characterization and synthesis of signed multivariate tail-dependence at finite thresholds, preserving the complete signed tail family throughout.
Linear memory stores associations up to a logarithmic scale, but listwise retrieval can handle a quadratic scale.
problem How many key-value associations can a linear memory store?
method Analyzed linear memory models for top-1 and listwise retrieval, proving phase transitions and developing asymptotic theories.
result Linear memory has a logarithmic capacity for top-1 retrieval and a quadratic capacity for listwise retrieval.
This paper optimizes performative risk by focusing on convex properties and developing efficient algorithms.
problem Performative risk, the loss experienced by decision makers, is not optimized by stable models.
method Identifying convex properties of loss function and model-induced distribution shift, developing algorithms for optimization.
result Optimization of performative risk with better sample efficiency than generic methods.
Plug-in method improves performative prediction accuracy.
problem Learning under performative feedback with slow convergence rates.
method Plug-in performative optimization using models.
result Plug-in method can be superior to model-agnostic strategies.
We present a new methodology of computing incremental contribution for performance ratios for portfolio like Sharpe, Treynor, Calmar or Sterling ratios. Using Euler's homogeneous function theorem, we are able to decompose these performance ratios as a linear combination of individual modified performance ratios. This a…
The computation of convolution layers in deep neural networks typically rely on high performance routines that trade space for time by using additional memory (either for packing purposes or required as part of the algorithm) to improve performance. The problems with such an approach are two-fold. First, these routines…
New causal models perform poorly when evaluated on biased training sets.
problem Sample selection bias affects the evaluation of causal models' prediction performance.
method Re-evaluated prediction performance of causal models on a genetic perturbation data set, proposing a less-biased evaluation set.
result Causal models have similar or worse performance when evaluated on a less-biased set compared to standard association-based estimators.
A new framework for performative prediction robust to distributional misspecification.
problem Performative prediction models can be influenced by their own predictions, leading to suboptimal outcomes.
method Introduces distributionally robust performative prediction (DRPO) to approximate the true performative optimum (PO) robustly.
result DRPO provides provable guarantees as a robust approximation to the true PO when the nominal distribution map is misspecified.
Study compares Islamic banks' accounting and market performance.
problem Assessing the relationship between Islamic banks' accounting and market performance.
method Selected six Islamic banks, collected data from 2009-2013, used random-effect models.
result Superior accounting performance does not correlate with superior market performance.
The study evaluates AI model performance measures for medical use.
problem Selecting appropriate performance measures for AI models in medical practice.
method Assessed 32 performance measures across five domains for binary outcomes.
result 17 measures are both proper and reflect decision-analytic performance.
SHIFT framework identifies subgroups with large ML model performance decay.
problem Large model performance decay in subgroups when deployed.
method Subgroup-scanning Hierarchical Inference Framework (SHIFT) for performance drift.
result SHIFT identifies interpretable subgroups with large performance decay and suggests targeted actions to mitigate it.
New framework for predicting decisions that influence their own outcomes.
problem Predictions that affect the outcomes they predict, leading to undesirable distribution shift.
method Risk minimization framework combining statistics, game theory, and causality.
result Necessary and sufficient conditions for retraining to converge to a performatively stable point of minimal loss.