Surveying probabilistic real algebraic geometry.
problem Classical problems in real algebraic geometry.
method Probabilistic perspective on classical topics.
result Modern approach to Hilbert's Sixteenth Problem.
On-device research index
arXiv research
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.
168,657 papers · 148 categories
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48 results for “classical randomness”
Research proves the semi-classical limit of Liouville conformal field theory, describing deterministic geometry from random fluctuations.
problem Proving the semi-classical limit of Liouville conformal field theory.
method Probabilistic definition of Liouville theory, proving existence of semi-classical limit, defining classical stress-energy tensor.
result Existence and description of the semi-classical limit in terms of a massive Gaussian free field with Robin boundary conditions.
Random Function Descentmath.OC
Random Function Descent improves optimization in high dimensions.
problem Lack of effective optimization methods in high-dimensional spaces.
method Introducing a 'random function' framework to optimize classical optimization problems.
result Random Function Descent (RFD) is a scalable optimization method that bridges Bayesian and classical optimization.
Single tree outperforms random forest in testing accuracy.
problem The challenge of improving single decision tree performance.
method Gradient-based entire tree optimization framework, scaled sigmoid approximation, numerical stability algorithm, subtree polish strategy.
result Optimized single tree outperforms classic random forest by 2.03% on average.
Information Entropy of the Financial Market: Modelling Random Processes Using Open Quantum Systemsq-fin.MF
The financial market entropy is modeled using open quantum systems.
problem Understanding entropy in financial market dynamics.
method Using Open Quantum Systems to model entropy gain in financial markets.
result Interesting non-classical results generated by relaxing assumptions.
On the effects of biased quantum random numbers on the initialization of artificial neural networksquant-ph
Study finds no significant difference in neural network weights with quantum random numbers.
problem Effects of biased quantum random numbers on neural network initialization.
method Empirical study using quantum hardware and classical pseudo-random numbers.
result No statistically significant difference found between quantum random numbers and other types.
Quantum algorithm speeds up nested expectation estimation by nearly quadratically.
problem Estimating repeatedly nested expectations with quantum computing.
method Proposes a quantum algorithm achieving nearly quadratic speedup over classical methods.
result Achieves nearly quadratic speedup for RNEs, up to logarithmic factors.
Modern ML methods show unexpected behaviors that contradict classical statistics.
problem Modern machine learning methods exhibit behaviors at odds with classical statistical intuitions.
method Comparison between fixed and random design settings in ML and statistics.
result Moving from fixed to random designs reveals new insights into bias-variance tradeoffs and overfitting.
Paper studies tensor models using random matrix theory.
problem Analyzing asymmetric order-d spiked tensor models with Gaussian noise.
method Uses variational definition of singular vectors and values, constructs equivalent spiked symmetric block-wise random matrix from tensor contractions.
result Characterizes asymptotic singular values and alignments of singular vectors with true spike components.
Random number generators (RNGs) that are crucial for cryptographic applications have been the subject of adversarial attacks. These attacks exploit environmental information to predict generated random numbers that are supposed to be truly random and unpredictable. Though quantum random number generators (QRNGs) are ba…
Quantum computers outperform classical methods in density modeling.
problem Density modeling with quantum computers.
method Quantum-classical separation for density modeling.
result Quantum computers offer a super-polynomial advantage over classical algorithms for density modeling.
Study benchmarks classical models over quantum in DeFi yield prediction.
problem Accurate yield and performance forecasting for DeFi liquidity allocation.
method Benchmarked six models on Curve Finance pools' historical data.
result Classical models, especially XGBoost, outperform quantum models.
We extend to the framework of locally -convex modules some results from classical convex analysis. Namely, randomized versions of Mazur lemma and Krein-Smulian theorem under mild stability properties are provided.
Study shows gap between uniform convergence and test error in random feature models.
problem Understanding the gap between uniform convergence and test error in random feature models.
method Analytical expressions for uniform convergence over norm balls, interpolators, and minimum norm interpolator risk derived and proved.
result Uniform convergence over interpolators still gives a non-trivial bound of test error even when classical uniform convergence is vacuous.
New proof shows rapid mixing for random walks on nilmanifolds.
problem Proving rapid mixing for random walks on nilmanifolds.
method Proved rapid mixing for almost all random walks generated by m translations on nilmanifolds under mild assumptions.
result For several classical classes of nilmanifolds, m=2 suffices for rapid mixing.
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for …
Paper introduces new approximations for lognormal sums, matching comonotonicity and moments.
problem Approximating sums of lognormal random variables accurately.
method Introduces new approximations based on weighted distribution theory, emphasizing comonotonicity and moment matching.
result Approximations perform better than classical methods, especially in the right tail of the distribution.
New model predicts dynamic volatility in uncertain financial markets.
problem Predicting dynamic volatility in financial markets with uncertainty.
method Generalized Barndorff-Nielsen and Shephard (BN-S) model considering delay and fuzziness.
result Effective prediction of dynamic volatility with improved performance.
A version of indifference valuation of a European call option is proposed that includes statistical regularities of nonstochastic randomness. Classical relations (forward contract value and Black-Scholes formula) are obtained as particular cases. We show that in the general case of nonstochastic randomness the minimal …
Paper explores grafting consistent estimators to improve Random Forest consistency.
problem Ensuring Random Forests are consistent despite their performance.
method Grafting consistent estimators onto a shallow CART.
result Grafted estimators provide a consistency guarantee and perform well empirically.
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for financial market than the classical one. A part of our analysis is devoted to study t…
Survey on strong convergence in random matrices and its applications.
problem Understanding convergence of random matrices to operators.
method Analysis of operator norms of noncommutative polynomials.
result New insights and applications in random graphs, geometry, and operator algebras.
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation tech…
We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in under random linear transformations. This allows us to compute probabilities of a…
LMMVAE improves VAE for correlated data by separating latent variables into fixed and random parts.
problem Correlated data in tabular and image datasets.
method Integrates random effects into VAE architecture, separating latent variables into fixed and random parts.
result Significant improvement in reconstruction error and likelihood loss on unseen data.
Introduces RPU to explain randomization preference in dynamic settings.
problem Explains preference for randomization in dynamic investment problems.
method Introduces recursive perturbed utility (RPU) to incorporate randomization preference.
result Proves RPU-optimal portfolio policy is Gaussian and can be expressed in closed form.
Survey on random walks on mapping class groups and their properties.
problem Understanding random walks on mapping class groups.
method Analyzing actions on Teichmüller spaces and curve complexes.
result Laws of large numbers and central limit theorems for random walks.
Study shows double descent curve in high-dimensional linear regression with random projections.
problem Understanding the generalization performance in high-dimensional settings with random projections.
method Fixed prediction problem, ridge regression estimator, minimum norm least-squares fit, random matrix theory, asymptotic equivalents.
result Exhibit a double descent curve for high-dimensional linear regression with random projections.
The paper outlines future work in random sets theory.
problem Developing a theory of statistical reasoning with random sets.
method Generalizing logistic regression, probability laws, and geometric uncertainty.
result A new geometric approach to uncertainty with general random sets.
Gradient descent and SGD solve nonlinear inverse problems efficiently.
problem Solving nonlinear inverse problems with random design.
method Gradient descent and SGD with mini-batching, under classical assumptions.
result Achieves optimal convergence rates in RKHS framework.
We study the statistical and computational aspects of kernel principal component analysis using random Fourier features and show that under mild assumptions, features suffices to achieve sample complexity. Furthermore, we give a memory efficient streaming algorithm based on classical Oja…
Abstract: Nonlinear random walk with distributionally robust transition probabilities.
problem Modeling nonlinear random walks with robust transition probabilities.
method Scaling limit and nonlinear semigroup approach.
result Explicit computation of the generator and corresponding PDE.
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The most important function is arguably the Euclidean distance between data items, …
We propose and study kernel conjugate gradient methods (KCGM) with random projections for least-squares regression over a separable Hilbert space. Considering two types of random projections generated by randomized sketches and Nyström subsampling, we prove optimal statistical results with respect to variants of norms …
Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphsstat.ML
Study on convergence of graph neural networks on random graphs.
problem Convergence of message passing graph neural networks on large random graphs.
method Extended convergence results to a broad class of aggregation functions using McDiarmid inequality.
result Non-asymptotic bounds for convergence quantified with high probability.
Formula found for probability of random triangles on flat tori being homotopically trivial.
problem Calculating the probability of random triangles on flat tori being homotopically trivial.
method Reduced problem to new invariant of measurable sets in the plane unchanged by area-preserving affine transformations.
result Probability is minimized on rectangular tori and maximized on regular hexagonal tori.
A new sampling method reduces computational cost for high-dimensional log-concave distributions.
problem High computational cost of ULMC in high dimensions.
method Random Coordinate ULMC (RC-ULMC) selects a single coordinate per iteration.
result RC-ULMC is cheaper than classical ULMC, especially in highly skewed and high-dimensional problems.
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from classical random walks analogs, in particular, they walk faster than classical o…
In this paper, we face the problem of simulating discrete random variables with general and varying distributions in a scalable framework, where fully parallelizable operations should be preferred. The new paradigm is inspired by the context of discrete choice models. Compared to classical algorithms, we add paralleliz…
The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A particular attention is paid to randomized estimators drawn in a small neighbor…
Analyzes bias-variance in overparameterized linear models using random features.
problem Understanding bias-variance trade-off in overparameterized models.
method Zero-temperature cavity method and random matrix theory.
result Three phase transitions in the linear random features model.
Differentially private random block coordinate descent improves utility in machine learning.
problem Lack of privacy in classical CD methods when handling sensitive information.
method Proposes a differentially private random block coordinate descent method using sketch matrices and importance sampling.
result Demonstrates improved convergence rates and utility guarantees compared to non-private methods.
Paper improves worst-case regret bounds for RLSVI in reinforcement learning.
problem Minimizing regret in reinforcement learning with randomized value functions.
method Introduces a clipping variant of Thompson Sampling for RLSVI.
result Achieves a worst-case regret bound.
A new sampling method, RC-LMC, reduces computational cost for high-dimensional log-concave distributions.
problem High computational cost of LMC in high dimensions.
method RC-LMC updates only one coordinate at a time, adding noise.
result RC-LMC is more efficient than LMC in high dimensions, especially for skewed distributions.
The paper solves MMV and MV problems with random coefficients and finds shared optimal strategies.
problem Optimal trading strategies with random market coefficients.
method Backward stochastic differential equations (BSDEs) to find optimal strategies.
result MMV and MV problems share the same optimal portfolio and value under random coefficients.
Symmetric observations don't necessarily imply symmetric causal explanations.
problem Inferring causal models from observed correlations is challenging and computationally intensive.
method An explicit example using a tripartite probability distribution over binary events.
result Symmetries in observations cannot be used to reduce the hypothesis space of causal models.
New method uses random convex polytopes to measure representation quality.
problem Measuring the quality of deep learning representations.
method Random Polytope Descriptor method based on random convex polytopes.
result Regularization in autoencoders can degrade out-of-distribution detection.
Extends RL to random stopping times, improving optimization.
problem Real-world applications with random stopping times.
method Extended RL framework to random stopping times, derived new formulas.
result Improves optimization convergence with new formulas.