We develop a new bound for estimating CVaR from samples of an unbounded random variable.
problem Estimating CVaR from i.i.d. samples of an unbounded random variable.
method Derive a one-sided concentration bound for a CVaR estimator.
result A novel concentration bound for CVaR estimation.
Framework creates fast, interpretable surrogates for stochastic simulators with unbounded randomness.
problem Creating accurate and fast approximations for stochastic simulators with unbounded randomness.
method Probabilistic surrogate networks that retain structure of reference simulators and enable amortized inference.
result Surrogates accurately model stochastic programs with unbounded random variables and significantly speed up inference.
Note improves confidence bounds for random variables.
problem Improving confidence bounds for random variables with unbounded ranges and different distributions.
method PAC-Bayes-ification of a derived confidence bound.
result Streamlined proofs for existing results.
We prove new concentration inequalities for random variables.
problem Concentration of random variables in nonlinear functions.
method Efron-Stein inequalities and PAC-Bayesian approach.
result User-friendly concentration bounds for various applications.
New inequalities for unbounded functions improve denoising score matching.
problem Statistical error bounds for denoising score matching with unbounded objective functions.
method Derive new concentration inequalities using McDiarmid's inequality and Rademacher complexity bounds.
result Improved statistical error bounds for denoising score matching.
This paper addresses sampling from bounded distributions using SGLD.
problem Sampling from models with bounded variables using SGLD.
method Introduces and evaluates various mapping techniques to transform unbounded samples into bounded ones.
result Invertible Lipschitz mappings overcame the pitfalls of existing methods and achieved weak convergence.
New PAC-Bayes bounds for unbounded losses using Cramér-Chernoff techniques.
problem Developing bounds for unbounded losses in PAC-Bayesian settings.
method Introducing a new PAC-Bayes oracle bound using Cramér-Chernoff bounds and controlling random variable tails.
result Our bounds generalize and improve upon previous results, providing more informative and potentially tighter bounds.
Proves new concentration inequalities for sub-gaussian and sub-exponential variables.
problem Understanding functions of independent random variables better.
method Sub-gaussian and sub-exponential conditions, Rademacher complexities, Lipschitz function classes.
result Extension of Rademacher complexities to unbounded sub-exponential distributions.
New bounds on continuous random variables' right-tail probabilities.
problem Finding precise upper and lower limits for right-tail probabilities of continuous random variables.
method Developed new bounds based on PDF, first derivative, and two parameters.
result The new bounds are tight for various continuous random variables.
Study shows convergence rate for empirical minimizer of unbounded functions with fast growth.
problem Convergence rate of empirical minimizer for unbounded functions with fast growth.
method Analyzes L1-distance convergence rate of the empiric minimizer for coercive functions sampled with noise. result Convergence rate is bounded above by ann−1/q, where q is the dimension and an=o(nε) for every ε>0. We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses from the beginning an additional information in the form of a random variable G, which only becomes known to the ordinary agents at date T, we give criteria for the No …
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in learning theory and generalization bounds for unbounded loss functions.
Paper analyzes KSG mutual information estimator for smooth distributions.
problem Analyzing the convergence rate of KSG estimator for smooth distributions.
method Adaptive recombination of KL entropy estimators analysis.
result Convergence rate of KSG estimator for smooth distributions is analyzed.
This memoir presents a systematic study of the utility maximization problem of an investor in a constrained and unbounded financial market. Building upon the work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a bounded framework, we extend our analysis to the more challenging unbounded case. Our methodolo…
In this paper, we analyze a real-valued reflected backward stochastic differential equation (RBSDE) with an unbounded obstacle and an unbounded terminal condition when its generator f has quadratic growth in the z-variable. In particular, we obtain existence, comparison, and stability results, and consider the opti…
New approach finds solutions to games with unbounded controls.
problem Existence of equilibrium in mean-field games with unbounded controls.
method Weak formulation and new existence/stability results for quadratic-growth generalized McKean-Vlasov BSDEs.
result Existence of equilibrium result for non-Markovian mean-field games with unbounded control space.
Solves open problem on universally consistent online learning with unbounded losses.
problem Open problem on universally consistent online learning with unbounded losses.
method Constructs random measurable partitions of the instance space.
result Simple memorization rule is optimistically universal for any unbounded loss.
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility maximization problems including the classical one…
We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endo…
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility-maximization problems including the classical one…
This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies -- t…
The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.
problem Gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.
method Establishes Bismut-type formulas and gradient estimates for Feynman--Kac semigroups on Riemannian manifolds with boundary, under geometric conditions formulated in terms of Ricci curvature and second fundamental form.
result Derives pointwise gradient estimates for the Neumann semigroup under variable, possibly unbounded, lower curvature bounds.
This paper completes the analysis of Choulli et al. Non-Arbitrage up to Random Horizons and after Honest Times for Semimartingale Models and contains two principal contributions. The first contribution consists in providing and analysing many practical examples of market models that admit classical arbitrages while the…
Solves consumption-investment problem with random horizon under Epstein-Zin preferences.
problem Maximizing consumption and investment under random time horizons with Epstein-Zin utility.
method Backward stochastic differential equations with superlinear growth on unbounded random horizons.
result Optimal strategies differ significantly when moving from fixed to random time horizons.
New algorithms optimize risk-aware selection in uncertain rewards.
problem Balancing expected reward and risk in uncertain, potentially heavy-tailed rewards.
method Distribution oblivious algorithms that consider CVaR, not bound on moments/tails.
result Provable upper bounds on incorrect identification probability.
New approach to concentration inequalities for unbounded state space dynamical systems.
problem Concentration inequalities for unbounded state space dynamical systems.
method Functional analytic framework, transport-entropy inequality.
result Exponential concentration inequalities for sampling from stationary distribution.
In this letter we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for Explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting…
Study proves boundedness of operators in variable exponent Morrey spaces.
problem Boundedness of operators in global Morrey-type spaces with variable exponents.
method Analysis of Hardy-Littlewood maximal operator and potential type operator in variable exponent Morrey spaces.
result Boundedness of the Hardy-Littlewood maximal operator and potential type operator in global Morrey-type spaces with variable exponents.
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce stable graphical (SG) models, a class of multivariate st…
Improved bounds for unbounded losses using transductive priors.
problem Sequential regression and classification with unbounded losses.
method Exponential weights algorithm with transductive priors.
result Statistical bounds independent of design vectors and optimal solution norm.
Paper proposes robust risk measures for non-negative risks with partial information.
problem Tackles robustness of distortion risk measures under distributional uncertainty.
method Introduces new uncertainty sets and derives closed-form expressions for risk maximization.
result Derives closed-form expressions for risk maximization over uncertainty sets.
New algorithm robust to probabilistic unbounded adversarial attacks in bandit problems.
problem Powerful adversaries that can catastrophically perturb the revealed reward in bandit problems.
method Proposes med-E-UCB and med-ε-greedy algorithms based on sample median for robustness. result Achieves O(logT) pseudo-regret under arbitrary and unbounded reward perturbation. This paper is devoted to obtaining a wellposedness result for multidimensional BSDEs with possibly unbounded random time horizon and driven by a general martingale in a filtration only assumed to satisfy the usual hypotheses, i.e. the filtration may be stochastically discontinuous. We show that for stochastic Lipschitz…
The contact graph of a CAT(0) cubical complex has unbounded structure and a Gaussian CLT for random walks.
problem Understanding the structure and behavior of random walks on CAT(0) cubical complexes.
method Proved the contact graph is unbounded and homeomorphic to the boundary. Reformulated Caprace-Sageev's theorem. Proved a Central Limit Theorem for random walks.
result A Central Limit Theorem for random walks on CAT(0) cubical complexes, with a non-degenerate Gaussian distribution.
Random subgroups in hyperbolic spaces have full limit sets and bounded critical exponents.
problem Understanding stationary random subgroups in hyperbolic spaces.
method Analyzing limit sets and critical exponents of random subgroups.
result Random subgroups have full limit sets and bounded critical exponents.
Study stability of contingent claim solutions under probabilistic perturbations.
problem Stability of solutions to discrete-time contingent-claim problems under uncertainty.
method Use Rockafellian perturbations to analyze stability of solutions.
result Establishes convergence of dual problems and shadow prices.
This paper studies the optimal consumption under the addictive habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov's multi-asset framework with a cash account. At the terminal time T, the investor can receive unb…
Efficiently estimates linear models robust to corrupted data.
problem Learning linear models under adversarial corruption and minimal distributional assumptions.
method Develops a polynomial relaxation of independence to achieve optimal convergence rate.
result Achieves optimal convergence rate of ε2−2/k for k-hypercontractive distributions. New bounds for statistical entropic optimal transport with subgaussian measures.
problem Establishing statistical bounds for entropic optimal transport.
method Proving sample complexity and central limit theorem for entropic OT.
result Improved convergence rate and central limit theorem for empirical measures.
This paper provides a PAC-Bayesian bound for CVaR in machine learning.
problem Learning algorithms minimizing CVaR of empirical loss.
method Generalization bound of PAC-Bayesian type, reducing CVaR estimation to expectation estimation.
result The bound is small when empirical CVaR is small, providing concentration inequalities for CVaR.
New bounds for causal effect identification in time series graphs with latent confounders.
problem Identifying causal effects in time series graphs with latent confounders over unbounded time intervals.
method Applying the Causal Identification algorithm to a constant-size segment of the time series graph.
result A bound on the number of past time steps needed for causal effect identification.
New algorithms solve stochastic variational inequalities without bounded variance assumption.
problem Solving stochastic variational inequalities without bounded variance assumption.
method Developed algorithms for two classes of problems: monotone and structured nonmonotone VIs.
result Oracle complexity of O(ε^-4) for solving VIs with unbounded domains and possibly unbounded variance.
This note shows how to transform high-probability to in-expectation guarantees in machine learning.
problem The challenge of constructing reliable machine learning models due to sampling randomness.
method Transforming high-probability to in-expectation guarantees using a witness condition for unbounded loss functions.
result A technical transformation method for generalization guarantees in machine learning.
Study on inequalities for multinomial variables.
problem Understanding concentration inequalities for multinomial variables.
method Investigation of Dirichlet and Multinomial random variables.
result Results on concentration inequalities for multinomial variables.
New stability framework relaxes boundedness assumptions for generalization bounds.
problem Overly restrictive assumptions for modern learning settings with heavy-tailed or unbounded losses.
method Develops a stability-based framework requiring only finite Lp moment conditions. result Sharp generalization bounds derived for various learning paradigms.
A real valued function φ of one variable is called a metric transform if for every metric space (X,d) the composition dφ=φ∘d is also a metric on X. We give a complete characterization of the class of approximately nondecreasing, unbounded metric transforms φ such that the trans…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operator-…
Sharp concentration results for sums of heavy-tailed random variables.
problem Analyzing sums of independent heavy-tailed random variables.
method Using concentration inequalities and large deviation principles for distributions satisfying specific tail bounds.
result Sharp concentration inequalities and large deviation results for sums of heavy-tailed random variables.