The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propag…
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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.
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48 results for “Concrete random variables”
Proposes a few-shot learning method for feature selection without labeled data.
problem Feature selection in unlabeled data with limited instances.
method Uses Concrete random variables and permutation-invariant neural networks to select features from multiple source tasks.
result Outperforms existing methods in feature selection performance.
Sequence-to-sequence text-to-speech (TTS) is dominated by soft-attention-based methods. Recently, hard-attention-based methods have been proposed to prevent fatal alignment errors, but their sampling method of discrete alignment is poorly investigated. This research investigates various combinations of sampling methods…
Paper studies second order tail probabilities in risk models.
problem Analyzing tail probabilities in risk models with constant interest force.
method Asymptotic expansion and weighted Kesten-type inequality for second order subexponential random variables.
result Second order asymptotic formulae for continuous-time renewal risk models are derived.
Discrete random variables are natural components of probabilistic clustering models. A number of VAE variants with discrete latent variables have been developed. Training such methods requires marginalizing over the discrete latent variables, causing training time complexity to be linear in the number clusters. By appl…
Statistical Microeconomicsq-fin.GN
A statistical generalization is made of microeconomics in the spirit of going from classical to statistical mechanics. The price and quantity of every commodity1 traded in the market, at each instant of time, is considered to be an independent random variable: all prices and quantities are considered to be stochastic p…
A framework for the generation of bridge-specific fragility utilizing the capabilities of machine learning and stripe-based approach is presented in this paper. The proposed methodology using random forests helps to generate or update fragility curves for a new set of input parameters with less computational effort and…
Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to produce the final model. The performance of variable screening depends on both com…
Improved efficiency in HMC samplers reduces dissipative behavior.
problem Reducing dissipative behavior in HMC samplers.
method Variable integration time and partial velocity refreshment.
result Efficiency improved by a √κ factor in Wasserstein-2 distance.
The interplay between the Hamilton-Jacobi theory of orthogonal separation of variables and the theory of group actions is investigated based on concrete examples.
In this paper we introduce a new parametric distribution, the Mixed Tempered Stable. It has the same structure of the Normal Variance Mean Mixtures but the normality assumption leaves place to a semi-heavy tailed distribution. We show that, by choosing appropriately the parameters of the distribution and under the conc…
The paper proposes a new method to measure risk with fine-grained tail sensitivity.
problem Risk measures that do not account for tail sensitivity are insufficient for machine learning systems.
method The approach involves specifying a reference distribution with desired tail behavior and constructing risk measures compatible with this upper probability.
result Risk measures with fine-grained tail sensitivity can replace the expectation operator in machine learning systems.
Develops statistical framework for analyzing functional data extremes.
problem Analyzing extremes of functional data in Hilbert spaces.
method Regular variation in Hilbert spaces, Peaks-Over-Threshold framework, functional PCA.
result Proposes a dimension reduction method for functional extreme observations.
We discuss the applications of Random Matrix Theory in the context of financial markets and econometric models, a topic about which a considerable number of papers have been devoted to in the last decade. This mini-review is intended to guide the reader through various theoretical results (the Marcenko-Pastur spectrum …
Recent theoretical work has established connections between over-parametrized neural networks and linearized models governed by he Neural Tangent Kernels (NTKs). NTK theory leads to concrete convergence and generalization results, yet the empirical performance of neural networks are observed to exceed their linearized …
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 for -hypercontractive distributions.
The study examines Fisher information matrices and neural tangent kernels for simple ReLU networks with random weights.
problem Understanding the relationship between Fisher information matrices and neural tangent kernels for 2-layer ReLU networks.
method Analyzes Fisher information matrices and neural tangent kernels for 2-layer ReLU networks with random hidden weights, focusing on spectral decomposition and eigenfunctions.
result Obtained an approximation formula for functions represented by 2-layer neural networks.
The present work constitutes the second part of a two-paper project that, in particular, deals with an in-depth study of effective techniques used in econometrics in order to make accurate forecasts in the concrete framework of one of the major economies of the most productive Italian area, namely the province of Veron…
The book explores stochastic areas and heat kernels on manifolds.
problem Understanding stochastic area functionals and heat kernels on manifolds.
method Study of Brownian motions and heat kernels on Lie groups and Riemannian manifolds.
result Rich interactions between stochastic calculus, geometry, and random matrices.
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary tim…
The paper calculates asymptotic expansions for specific types of oscillatory integrals.
problem Analyzing oscillatory integrals with complex phase functions.
method Using asymptotic expansions of simpler phase functions to derive results for more complex cases.
result Explicit computation of coefficients in asymptotic expansions for certain integrals.
We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain somewhat obscure. By analyzing a number of concrete examples, we show that low-comp…
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.
Paper extends stochastic dominance for compound binomial distributions.
problem Stochastic dominance for infinite-mean random variables.
method Investigates properties and inclusion relationships of distribution classes, extends results to compound binomial distributions.
result Establishes necessary and sufficient conditions for first-order stochastic dominance preservation.
We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatial-temporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques based on Gaussian processes and co-Kriging. While the Gaussian prior assumption…
New tree-structured Markov fields with Poisson marginals for counting variables.
problem Counting variables with complex dependencies.
method Tree-structured Markov random fields with Poisson marginals.
result Straightforward sampling and joint probability calculations.
This article reviews and explains HMC-based methods for sampling constrained continuous distributions.
problem Sampling from continuous distributions with constraints.
method HMC and related methods for constrained sampling.
result HMC and related methods are more efficient for constrained sampling.
We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain somewhat obscure. By analyzing a number of concrete examples, we show that low-comp…
This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do…
PROD method improves high-dimensional regression by handling strong correlations.
problem Violation of Irrepresentable Condition in LASSO for high-dimensional data.
method PROD procedure based on orthogonal decomposition of design matrix.
result PROD enhances performance of high-dimensional penalized regression.
This work is the first part of a project dealing with an in-depth study of effective techniques used in econometrics in order to make accurate forecasts in the concrete framework of one of the major economies of the most productive Italian area, namely the province of Verona. In particular, we develop an approach mainl…
Weakly-supervised learning is a paradigm for alleviating the scarcity of labeled data by leveraging lower-quality but larger-scale supervision signals. While existing work mainly focuses on utilizing a certain type of weak supervision, we present a probabilistic framework, learning from indirect observations, for learn…
New class of heavy-tailed distributions shows weighted averages dominate individual variables.
problem Understanding and comparing risks in heavy-tailed distributions.
method Introducing a new class of heavy-tailed distributions and proving stochastic dominance relations.
result Weighted averages of random variables in this class are stochastically larger than individual variables.
Consider an experiment involving a potentially small number of subjects. Some random variables are observed on each subject: a high-dimensional one called the "observed" random variable, and a one-dimensional one called the "outcome" random variable. We are interested in the dependencies between the observed random var…
On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examplesmath.PR
We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a non-deterministic and time inhomogeneous compensator. The BSDE generator function c…
Diversification improves profits for heavy-tailed investments.
problem Investment portfolios of Pareto-distributed returns.
method Stochastic dominance and majorization order.
result Diversification increases first-order stochastic dominance for heavy-tailed returns.
The paper sets limits on the accuracy of macroeconomic forecasts based on statistical moments and trade volumes.
problem Uncertainty in predicting macroeconomic variables like prices and returns.
method Defines theoretical lower bounds of uncertainty and upper limits on forecast accuracy based on statistical moments and trade volumes.
result Accuracy of forecasts of probabilities of macroeconomic variables doesn't exceed Gaussian approximations.
We investigate concentration inequalities for Dirichlet and Multinomial random variables.
This study compares machine learning methods for high-cardinality categorical variables.
problem Machine learning struggles with high-cardinality categorical variables.
method Empirical comparison of tree-boosting, deep neural networks, and linear mixed effects models.
result Tree-boosting with random effects outperforms deep neural networks with random effects.
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo me…
Random Forest variable importance is improved by class balancing techniques.
problem Class imbalance problem in machine learning.
method Proposed a variable selection algorithm using RF variable importance and its confidence interval.
result Our algorithm efficiently selects an optimal feature set, leading to improved prediction performance.
A note on extending Chernoff bound for unit interval random variables.
problem Extending the Chernoff bound to random variables in the unit interval.
method Proof of extension of the Chernoff bound.
result A proof provided for the extension of the Chernoff bound.
This paper examines from an experimental perspective random forests, the increasingly used statistical method for classification and regression problems introduced by Leo Breiman in 2001. It first aims at confirming, known but sparse, advice for using random forests and at proposing some complementary remarks for both …
Hashing is a basic tool for dimensionality reduction employed in several aspects of machine learning. However, the perfomance analysis is often carried out under the abstract assumption that a truly random unit cost hash function is used, without concern for which concrete hash function is employed. The concrete hash f…
AugBagg improves random forest accuracy with added noise variables.
problem Improving model accuracy with random forest.
method AugBagg procedure using additional noise variables.
result Out-of-sample predictive accuracy improved with AugBagg.
Paper generalizes bipolar theorems for non-negative random variables.
problem Problems with existing bipolar theorems under stronger assumptions.
method Generalizes existing theorems in a robust probabilistic framework.
result Provides necessary and sufficient conditions for bipolar representation.
Generative model learns conditional distributions on collective variable levels.
problem Modeling conditional probability distributions on collective variable levels.
method General and efficient learning approach, data enrichment strategy.
result Effective generative models on different level-sets of collective variables.
A New Type Of Upper And Lower Bounds On Right-Tail Probabilities Of Continuous Random Variablesmath.PR
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.