This paper develops a method to estimate the rate-distortion function for general data sources.
problem Estimating the rate-distortion function for general data sources.
method Develops an algorithm for sandwiching the R-D function of a general (not necessarily discrete) source using i.i.d. data samples.
result Estimates R-D sandwich bounds for various data sources, including natural images, indicating potential for improving compression methods.
We apply Gromov's ham sandwich method to get (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in a Euclidean space.
In this paper, we propose new efficient algorithms to verify the null space condition in compressed sensing (CS). Given an (n−m)×n (m>0) CS matrix A and a positive k, we are interested in computing αk={z:Az=0,z=0}max{K:∣K∣≤k}max ∥zK∥1∥z∥1, where …
The main goal of the paper is to prove the sandwich theorem for geodesic convex functions in a complete Riemannian manifold. Then by using this theorem we have proved an inequality in a manifold with bounded sectional curvature. Finally, we have shown that the gradient of a convex function is orthogonal to the tangent …
New financial model with sandwiched volatility for option pricing.
problem Developing a new financial model for option pricing.
method Introducing a new model with stochastic volatility driven by a Gaussian Volterra process, ensuring the solution is sandwiched between two arbitrary Hölder continuous functions.
result Developed an algorithm for pricing options with discontinuous payoffs using Malliavin calculus.
Study symplectic fillings of sandwiched singularities.
problem Contrast deformation theory and symplectic topology of Milnor fibers.
method Develop an analog of de Jong--van Straten's theory in the symplectic setting using spinal open books and nearly Lefschetz fibrations.
result Minimal symplectic fillings of links are generated by certain immersed disk arrangements.
Computing the marginal likelihood (ML) of a model requires marginalizing out all of the parameters and latent variables, a difficult high-dimensional summation or integration problem. To make matters worse, it is often hard to measure the accuracy of one's ML estimates. We present bidirectional Monte Carlo, a technique…
Invariant measures found for contact Hamiltonian systems split into Reeb and Liouville dynamics.
problem Finding invariant measures for contact Hamiltonian systems.
method Splitting the system into Reeb and Liouville dynamics; using invariant measures and symplectic sandwiches.
result Invariant measure found for Reeb dynamics; characterization of Liouville dynamics invariant measure.
In this paper we show the validity, under certain geometric conditions, of Wheeler's thin sandwich conjecture for higher dimensional theories of gravity. We extend the results shown by R. Bartnik and G. Fodor for the 3-dimensional case in two ways. On the one hand, we show that the results obtained by the mentioned aut…
We show that the if a sequence of normalized polynomials gives rise to a positive basis of the skein algebra of a surface, then it is sandwiched between the two types of Chebyshev polynomials. For the closed torus, we show that the normalized sequence of Chebyshev polynomials of type one (T^n) is the only one w…
Equivalent formulations for low-rank matrix optimization are proven.
problem Low-rank matrix optimization with rank constraints.
method Established geometric landscape connections between manifold and factorization formulations.
result Equivalence between manifold and factorization formulations at FOSPs, SOSPs, and strict saddles.
Maximal extractable value in CFMMs can degrade or improve routing quality, with reordering MEV showing logarithmic impact.
problem Maximal extractable value in constant function market makers (CFMMs) and its impact on routing quality.
method Game theoretic analysis of MEV in CFMMs, constructing price of anarchy and analyzing reordering MEV.
result Conditions under which reordering MEV shows logarithmic impact, and implications for MEV searchers and CFMM designers.
In an L∞-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems derived by a reasonable restriction of the class of equivalent martingale measures…
Paper proves SVV model reproduces power-law skew in implied volatilities.
problem Reproducing power-law behavior in implied volatility skew.
method Analytical proof using Malliavin calculus and Volterra kernel selection.
result SVV model reproduces power-law skew under correct kernel choice.
Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician takes a first step in this direction, by employing a kernel search algorithm with Gaussian Processes (GP) to provide interpretable statistical models for regression problems. However this does not scale due …
A theorem divides hyperplanes evenly with a line through the origin.
problem Dividing hyperplanes evenly with a line.
method Direct proof using measures on hyperplanes.
result A line through the origin divides hyperplanes evenly.
The reduced thin-sandwich equations (RTSE) appear within Wheeler's thin-sandwich approach towards the Einstein constraint equations (ECE) of general relativity. It is known that these equations cannot be well-posed in general, but, on closed manifolds, sufficient conditions for well-posedness have been established. In …
Recent work has suggested enhancing Bloom filters by using a pre-filter, based on applying machine learning to determine a function that models the data set the Bloom filter is meant to represent. Here we model such learned Bloom filters,, with the following outcomes: (1) we clarify what guarantees can and cannot be as…
Polyak-Ruppert CLT for SA-Adam with momentum and non-convergent adaptive preconditioning
problem Adaptive optimizers combining momentum and non-convergent preconditioning
method Proving positive drift stability and a non-autonomous Polyak-Ruppert CLT for SA-Adam
result The iterate-marginal covariance is exactly the plain stochastic gradient descent (SGD) sandwich
Paper introduces f-divergence variational inference for broader application.
problem Variational inference limited to specific divergences.
method Generalizes variational inference to all f-divergences using f-divergence minimization.
result Unified framework for variational inference with arbitrary f-divergences.
Study reveals risks of investing in new crypto-tokens in decentralized exchanges.
problem Risks associated with investing in newly created tokens in decentralized exchanges.
method Analysis of financial impact, market dynamics, profitability, and liquidity manipulations.
result Significant market liquidity trapped in honeypots, reducing market efficiency and misleading investors.
Semi-implicit variational inference (SIVI) is introduced to expand the commonly used analytic variational distribution family, by mixing the variational parameter with a flexible distribution. This mixing distribution can assume any density function, explicit or not, as long as independent random samples can be generat…
Proposes a method for valid inference in GPLSIMs with longitudinal data.
problem Challenges in longitudinal data inference due to within-subject correlation and unstable variance estimation.
method Profile estimating-equation approach using spline approximation and block empirical likelihood.
result Block empirical likelihood ratio statistic with Wilks-type chi-square limit for joint inference.
Ethereum block builders can earn up to $14M/month by reordering transactions, harming users.
problem Block builders can exploit transaction reordering to earn significant profits, harming users.
method Estimation of MEV payments and analysis of reordering effects.
result Block builders can earn up to $14M/month by reordering transactions, skewing the distribution.
A new upper bound for variational inference improves the efficiency of Bayesian deep learning.
problem Improving variational inference in Bayesian deep learning.
method Presented a new upper bound (EUBO) for evidence, derived from KL-divergence and log marginal likelihood, and used SGD for optimization.
result The new upper bound (EUBO) is tighter than previous methods and outperforms state-of-the-art results in Bayesian neural networks.
Guaranteed bounds for posterior inference in probabilistic programs.
problem Approximating the posterior distribution of probabilistic programs with provable correctness.
method Interval-based trace semantics, soundness and completeness proofs, weight-aware interval type system.
result Guaranteed bounds on the posterior distribution of probabilistic programs are computed and proven to be correct.
Study on deformations of symmetric spaces using Jordan algebras.
problem Deformability of symmetric Einstein metrics on compact Lie algebras.
method Developed sandwich operators and quadratic Casimir operators for compact Lie algebras; calculated obstruction integrals from invariant polynomials; explored relation to simple Jordan algebras.
result Proved the nonlinear instability of most infinitesimally deformable irreducible compact symmetric spaces.
We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference …
Study finds average 2.02 bps loss in automated market maker routing.
problem Measuring sub-optimality in automated market maker routing.
method Three reproducible optimal benchmarks: SCO, FVO, G-FVO; bisection-based algorithm for optimal routing.
result Average 2.02 bps loss per trade, \$24 million total loss.
The study examines how backrun auctions can protect traders from price manipulation.
problem Price manipulation by arbitrageurs in batched trading venues.
method Developed a laminated queueing model to study price manipulation and introduced a price manipulation coefficient.
result Bound the price manipulation coefficient and found it approximated by a 'zeta value' with measurable parameters.
Motivated by the study of Q-learning algorithms in reinforcement learning, we study a class of stochastic approximation procedures based on operators that satisfy monotonicity and quasi-contractivity conditions with respect to an underlying cone. We prove a general sandwich relation on the iterate error at each time,…
Variational inference (VI) is widely used as an efficient alternative to Markov chain Monte Carlo. It posits a family of approximating distributions q and finds the closest member to the exact posterior p. Closeness is usually measured via a divergence D(q∣∣p) from q to p. While successful, this approach al…
To better understand the interplay of censoring and sparsity we develop finite sample properties of nonparametric Cox proportional hazard's model. Due to high impact of sequencing data, carrying genetic information of each individual, we work with over-parametrized problem and propose general class of group penalties s…
Study Stein and Milnor fillings of links from surface singularities.
problem Comparing Stein and Milnor fillings of links from surface singularities.
method Analyzing the topology and obstructions of Stein fillings and Milnor fillings.
result Milnor fillings have bounded topology, while Stein fillings can be more varied.
Paper improves ML estimation from incomplete data with robust M-estimator.
problem Estimating parameters from incomplete data with improved accuracy.
method Developed a robust M-estimator and a sandwich estimator for standard errors.
result Improved estimation accuracy with smaller standard errors than ML estimates.
Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation systems, multilabel learning, dictionary learning, etc. This paper examines a g…
The study connects projective codes to the distribution of zeros of odd maps.
problem Understanding the distribution of zeros of odd maps from spheres to Euclidean space.
method Using the topology of the space of probability measures on the sphere.
result Generalization of the Borsuk-Ulam theorem and its four consequences.
Researchers develop a method to infer reference measures from observed functionals.
problem Tackles the challenge of identifying or recovering a reference measure from observed functionals.
method Uses the property of law-invariant functionals defining lower or upper supporting sets in dual spaces of signed measures.
result Illustrates the methodology with examples and develops a modification for Value-at-Risk.
The paper improves confidence set construction for statistical inference.
problem Constructing reliable confidence sets in statistical inference.
method Establishes a finite-sample bound using effective dimension and generalized self-concordance.
result Developed a confidence set adapted to optimization landscapes.
New framework improves option pricing models by addressing volatility dynamics.
problem Challenges in standard option pricing models, especially in deriving implied volatility.
method Developed a new framework called Implied Remaining Variance (IRV), identifying minimal conditions for absence of arbitrage.
result Reformulated results of Schweizer and Wissel (2008b) and independently derived El Amrani, Jacquier and Martini (2021) results within IRV framework.
The paper explores handlebody versions of various diagram algebras.
problem None explicitly stated, but related to algebraic structures.
method Study of handlebody versions of classical diagram algebras and reformulation of cellular algebras.
result All mentioned algebras are part of the reformulated cellular algebra theory.
Study examines stylized facts in DEX markets vs. traditional exchanges.
problem Comparing stylized facts in decentralized exchanges (DEXs) vs. traditional markets.
method Empirical analysis of 24 most active Uniswap v3 pools.
result New statistical regularities in DEX markets, linked to market structure and activity.
New method reduces cloud usage for mobile/IoT predictions.
problem Minimizing cloud usage for mobile/IoT predictions while maintaining accuracy.
method Formulating the BL problem via bracketing functions h−,h+ from a simple class. result Improved performance over prior methods, validated on real-world datasets.
Optimizes portfolio in volatile markets with jumps, providing accurate formulas.
problem Optimizing wealth in a volatile financial market with jumps.
method Analyzes an incomplete stochastic volatility model, derives closed-form portfolio formulas using HJB equation and super-solution/sub-solution.
result Proves accuracy of derived portfolio formulas for both small and finite time horizons.
Generative Adversarial Networks (GAN) can achieve promising performance on learning complex data distributions on different types of data. In this paper, we first show a straightforward extension of existing GAN algorithm is not applicable to point clouds, because the constraint required for discriminators is undefined…
For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a "sandwiched" process consisting of a p…
Study optimizes prediction error for growing-dimensional PFLM models.
problem Optimizing prediction error for growing-dimensional PFLM models.
method Penalized least-squares approach in RKHS with effective dimension consideration.
result Shows exact upper bound for excess prediction risk in non-asymptotic form.
This paper optimizes liquidation strategies in DeFi protocols to prevent MEV attacks.
problem Predatory price manipulations and Maximal Extractable Value (MEV) attacks in DeFi protocols.
method Dynamic program modeling, Constant Product Market Maker (CPMM) transaction fees analysis.
result CPMM transaction fees make liquidation manipulations unprofitable for attackers.