The article provides formulas to hedge impermanent loss in decentralized markets.
problem Impermanent loss in concentrated liquidity provision in decentralized markets.
method Analytical characterizations and static replication formulas using European calls or puts.
result Static replication formulas accurately hedge impermanent loss.
Optimizes liquidity provision intervals for profitable AMM participation.
problem Financial losses from poor liquidity provision intervals and reallocation costs.
method Developed a tractable stochastic optimization problem.
result Computes optimal liquidity provision intervals for profitable liquidity concentration.
Improved privacy-preserving methods for convex optimization with heavy-tailed data.
problem Privacy-preserving optimization of convex functions with heavy-tailed data.
method Developed algorithms for private mean estimation and convex optimization under concentrated differential privacy constraints.
result Achieved improved upper bounds on excess population risk for convex and strongly convex loss functions.
Motivated by liquidity risk in mathematical finance, D. Lacker introduced concentration inequalities for risk measures, i.e. upper bounds on the \emph{liquidity risk profile} of a financial loss. We derive these inequalities in the case of time-consistent dynamic risk measures when the filtration is assumed to carry a …
Paper optimizes liquidity provision in decentralized finance markets.
problem Strategic LPs face predictable losses and concentration risk in CL pools.
method Derive optimal liquidity provision strategy based on fees, PL, and concentration risk.
result Optimal strategy increases fee revenue and profit from marginal rate changes.
Quantum models face barren plateaus, but specific losses can be trainable.
problem Barren plateaus and loss concentration in quantum generative models.
method Investigated explicit and implicit losses, and their interplay.
result Explicit losses lead to new barren plateaus, while implicit losses can be trainable.
Framework to generalize impermanent loss for decentralized exchanges.
problem Difficult analysis of impermanent loss due to diverse market maker algorithms and fee structures.
method Developed a framework to generalize impermanent loss for constant function market makers with optional concentrated liquidity.
result Identified conditions for profitability of liquidity provisioning.
The problem of estimating a high-dimensional sparse vector θ∈Rn from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage estimator, derived using a Bernoulli-Gaussian prior, is analyzed and compared with the…
We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function. We obtain sharp error rates even when concentration is false or is very restricted, for example, in heavy-tailed scenarios. Our results show that the error rate depends on two parameters: one captu…
Deep learning method improves risk assessment for small loan portfolios.
problem Measuring name concentration risk in small loan portfolios.
method Deep learning approach using Monte Carlo simulations with importance sampling.
result New method outperforms existing analytical methods for small portfolios.
Study improves PM concentration forecasting using MCCR loss.
problem Forecasting particulate matter concentration in South Korea.
method Used MCCR loss for regression analysis of air pollution and weather data.
result MCCR loss is more effective for extreme value forecasting.
This work uses statistical mechanics to explain AI learning.
problem Understanding the statistical principles behind AI learning.
method Starting from sample concentration behaviors, the study applies statistical mechanics principles to AI and machine learning.
result Exponential families and statistical quantities are key in AI and machine learning.
The paper proves LOO CV is reliable under estimator stability.
problem Ensuring the reliability of leave-one-out cross validation.
method Using concentration inequalities based on logarithmic Sobolev inequality.
result LOO CV is a valid procedure under estimator stability.
This paper shows DPPs can outperform random coresets in machine learning tasks.
problem Building efficient coresets for machine learning models.
method Using determinantal point processes (DPPs) to construct coresets with provable improvements over random sampling.
result DPPs can provably outperform independently drawn coresets in terms of approximation of total loss.
OEUVRE estimates online loss with constant time and memory, outperforming other methods.
problem Accurately estimating expected loss in online learning.
method Recursive evaluation of each sample on current and previous models, using algorithmic stability for updates.
result Consistency, convergence rates, and concentration bounds proved for OEUVRE.
This work explores the characteristics of financial contagion in networks whose links distributions approaches a power law, using a model that defines banks balance sheets from information of network connectivity. By varying the parameters for the creation of the network, several interbank networks are built, in which …
Optimizes liquidity provision in decentralized exchanges with utility indifference market makers.
problem Impermanent loss in decentralized exchanges without transaction fees.
method Mathematical formulation of liquidity provision, focusing on utility indifference market makers.
result No-arbitrage conditions and optimal arbitrage strategies are established.
The study examines the generalization of Macro-AUC in multi-label learning, identifying label imbalance as a critical factor.
problem Theoretical understanding of Macro-AUC in multi-label learning is lacking.
method Characterization of generalization properties of learning algorithms based on surrogate losses w.r.t. Macro-AUC, identification of label imbalance as a critical factor.
result The widely-used univariate loss-based algorithm is more sensitive to label imbalance than pairwise and reweighted loss-based ones, implying worse performance.
In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional Value-at-Risk (CVaR) is a popular risk measure for modeling the aforementioned objec…
Paper provides finite-sample guarantees for Wasserstein DRO without dimensionality curse.
problem Tackles empirical success of Wasserstein DRO in operations and ML with performance guarantees.
method Develops non-asymptotic framework for analyzing out-of-sample performance and generalization bound.
result First finite-sample guarantee for generic Wasserstein DRO problems without curse of dimensionality.
Piecewise linear activations create many spurious local minima in neural networks.
problem Understanding the loss surface of neural networks with piecewise linear activations.
method Proved the existence of infinite spurious local minima and partitioned the loss surface into smooth cells.
result Piecewise linear activations create many spurious local minima that are invariant under a continuous path.
Paper develops a new local convexity condition for non-isolated minima in non-convex optimization.
problem Lack of theory for non-isolated minima in non-convex optimization.
method Formulates a new local convexity condition and studies SGD convergence under this condition.
result Shows SGD can converge locally under the new condition.
We obtain sharp bounds on the performance of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without assuming that class members and the target are bounded functions or have rapidly decaying tails. Rather than resorting to a concentration-based argument, the method used her…
New method uses machine learning to estimate drug parameters in brain models.
problem Estimating unknown parameters in complex brain drug models.
method Physics-Informed Neural Networks (PINNs) for inverse problem solving.
result Accurate parameter estimation leads to precise drug concentration profiles.
Paper improves MMD estimation for analytical mean embeddings.
problem Improving MMD estimation for distributions with analytical mean embeddings.
method Proposes a tighter concentration result for MMD estimation under semi-explicit settings and extends to unbounded kernels.
result Demonstrates efficiency in real-world applications like index replication and calibration.
This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelets basis functions and calculate the coefficients of the approximation by inverting its Laplace transfor…
We solve ReLU regression with efficient approximations for various distributions.
problem Finding the best fitting ReLU function with square loss from unknown distributions.
method Introduced efficient constant-factor approximation algorithm and polynomial-time approximation scheme.
result First constant-factor approximation algorithm for ReLU regression with weak concentration conditions.
Developing an Agent-Based Model to Mitigate Adverse Selection in Uniswap v3 Liquidity Providers
problem Adverse selection in Uniswap v3 liquidity providers
method Agent-Based Model incorporating blockchain microstructure and volatility dynamics
result Dynamic fee schedules improve hedged Profit and Loss for liquidity providers
Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward numerical models. We present a physics-informed deep neural networks (DNNs) machine lea…
We prove semi-empirical concentration inequalities for random variables which are given as possibly nonlinear functions of independent random variables. These inequalities describe concentration of random variable in terms of the data/distribution-dependent Efron-Stein (ES) estimate of its variance and they do not requ…
Novel method reconstructs liquidity data for CLMMs, optimizing dynamic liquidity strategies.
problem Challenges in evaluating and optimizing CLMMs due to lack of historical liquidity data.
method Reconstructs historical liquidity states from swap transaction data using machine learning.
result Identifies outperformance of dynamic liquidity strategies over uniform allocation benchmarks.
New inequality for ternary variables improves on existing measures.
problem Analyzing excess losses and weighted majority votes with ternary random variables.
method Developed a split-kl inequality and its PAC-Bayes extension.
result Outperforms existing inequalities in certain regimes.
Enhances crypto-asset AMM with deep learning for better liquidity and efficiency.
problem Reduced slippage and improved liquidity in decentralized finance.
method Deep reinforcement learning for predicting market equilibrium and optimizing liquidity.
result Improved capital efficiency and reduced slippage for crypto-asset traders.
This guide simplifies high-probability regret bounds in empirical risk minimization.
problem High-probability regret bounds in empirical risk minimization.
method Modular presentation, three-step recipe, localized Rademacher complexity, local maximal inequalities, metric-entropy integrals.
result Recover familiar rates for various function classes and derive regret bounds for nuisance components.
Valid p-value for bounded random variables without distributional assumptions.
problem Calibration of predictive algorithms in a distribution-free setting.
method Built a super-uniform p-value based on a concentration inequality.
result Super-uniform p-value is tighter than existing alternatives.
We explore geometric aspects of bubble convergence for harmonic maps. More precisely, we show that the formation of bubbles is characterised by the local excess of curvature on the target manifold. We give a universal estimate for curvature concentration masses at each bubble point and show that there is no curvature l…
SCOPE estimator improves covariance and precision matrix estimation.
problem Estimating covariance and precision matrices accurately.
method Distributionally robust optimization with convex spectral divergence.
result SCOPE estimator reduces spectral bias and improves condition number.
This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used for approximate minimization of smooth and strongly convex losses, and specificall…
Previous work shows that adversarially robust generalization requires larger sample complexity, and the same dataset, e.g., CIFAR-10, which enables good standard accuracy may not suffice to train robust models. Since collecting new training data could be costly, we focus on better utilizing the given data by inducing t…
Study improves convergence rates for GVI under prior misspecification.
problem Improving convergence rates for GVI under prior misspecification.
method Proves rates of convergence and robustness to prior misspecification in GVI framework.
result Establishes sufficient conditions for existence and uniqueness of GVI posteriors.
Adversarial training improves robustness of halfspaces in noisy data.
problem Learning robust halfspaces in the presence of label noise.
method Adversarial training with binary cross-entropy or nonconvex sigmoidal loss.
result Adversarial training yields robust halfspaces with improved classification error.
Our work connects parameter magnitudes and Hessian eigenspaces in deep neural nets.
problem Understanding the relationship between parameter magnitudes and Hessian curvature in deep learning models.
method Developed a matrix-free algorithm based on sketched SVDs to measure similarity between parameter masks and Hessian eigenspaces.
result Top Hessian eigenvectors tend to be concentrated around larger parameters, indicating a connection between parameter magnitudes and loss curvature.
SGD noise helps select flat minima by concentrating in sharp directions and being proportional to loss value.
problem Understanding the implicit regularization of SGD and selecting flat minima in over-parameterized models.
method Relating SGD's linear stability to the Frobenius norm of the Hessian and analyzing the alignment property of SGD noise.
result Flat minima are linearly stable for SGD, and their sharpness is bounded independently of model size and sample size.
New method improves deep learning models in noisy label classification.
problem Improving deep learning models in noisy label classification.
method Analyzes loss and uncertainty changes during training, designs a new robust training method.
result Significantly outperforms other state-of-the-art methods in various deep learning models.
The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied nonconvex loss functions, but only considered the generalization error of the SGD in…
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 metric to measure liquidity position PNL, delta hedging algorithm for automated market makers.
problem Vulnerability of liquidity positions to price changes in underlying assets.
method Proposes a new metric for measuring PNL, delta hedging algorithm for various AMMs.
result New metric more accurately measures net value change due to price movement.
Method generates plausible financial stress scenarios using large deviations.
problem Misleading risk management by overlooking or overemphasizing implausible scenarios.
method Exploits large-deviations principle to concentrate risk factors near most likely stress configurations.
result Can generate informative stress scenarios even with limited historical data.