Incorporates matrix exponential into generative flows for improved performance.
problem Improving generative flow models for better density estimation.
method Integrates matrix exponential into generative flows, proposing new layers and modifying network architecture.
result The proposed model achieves great performance on density estimation.
New linear flows using exponential of linear transformations improve generative models.
problem Improving generative models in machine learning.
method Developed convolution exponentials and generalized Sylvester Flows using the exponential of linear transformations.
result Convolution exponentials and Convolutional Sylvester Flows outperform other models in log-likelihood.
The study explores generalized divergences and exponential families with a focus on sufficient conditions and laws of large numbers.
problem Generalization of Kullback-Leibler divergence and exponential families.
method Investigation of (h,τ)-divergence and (h,τ)-exponential families, definition of (h,τ)-dependence, proof of law of large numbers. result Sufficient condition for (h,τ)-divergence to induce Hessian structure on (h,τ)-exponential family, proof of law of large numbers. Paper introduces kernel deformed exponential families for sparse continuous attention.
problem Creating efficient attention mechanisms for sparse data.
method Developed kernel deformed exponential families, theoretically and experimentally.
result Kernel deformed exponential families can attend to multiple compact regions of data.
Groups on CAT(0) cube complexes grow exponentially uniformly.
problem Uniform exponential growth of groups acting on CAT(0) cube complexes.
method Study groups acting without global fixed points on CAT(0) square complexes.
result Groups with uniform exponential growth or stabilize Euclidean subcomplexes.
The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity pattern of the optimal parameter. This work characterizes a certain strong conve…
New exponential map for Lie groups connects to sub-Riemannian geometry.
problem Developing a new exponential map for Lie groups.
method Introducing a new exponential map related to sub-Riemannian geometry.
result New exponential map connects to sub-Riemannian geometry.
New insights into natural exponential families improve regret bounds for bandit problems.
problem Improving regret bounds for bandit problems with subexponential tails.
method Proving self-concordance for natural exponential families and applying to bandits.
result Optimistic algorithms for generalized linear bandits have second-order regret bounds that are free of an exponential dependence on problem parameters.
Introduces a new theoretical framework for exponential smoothing.
problem Theoretical foundation and robustness of simple exponential smoothing.
method Stochastic gradient ascent to optimize Gaussian log-likelihood functions.
result Simple exponential smoothing converges to the trend of a trend-stationary process.
Maximum likelihood learning with exponential families leads to moment-matching of the sufficient statistics, a classic result. This can be generalized to conditional exponential families and/or when there are hidden data. This document gives a first-principles explanation of these generalized moment-matching conditions…
We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models [Yang et al. 2015] did not allow positive dependencies for the exponential and Poisson generalizat…
EFDA extends LDA to non-Gaussian models using exponential families.
problem Classifying non-Gaussian data with LDA's limitations.
method EFDA uses exponential families to derive closed-form estimators for natural parameters and a linear decision rule.
result EFDA matches LDA's accuracy while reducing ECE by 2-6x, proving asymptotic calibration and efficiency.
Boosting with tempered exponential measures improves AdaBoost's convergence rate.
problem Improving the convergence rate of AdaBoost.
method Introducing tempered exponential measures (TEMs) to generalize AdaBoost's approach.
result t-AdaBoost achieves an improved convergence rate compared to AdaBoost, especially for t∈[0,1). A new machine learning model uses matrix exponentials for universal approximation.
problem Developing a robust and efficient machine learning model.
method Introduces a novel architecture using matrix exponentials as the only nonlinearity.
result The model achieves universal approximation properties and outperforms other models on benchmark tasks.
Exponential proportion of pseudo-Anosovs in mapping class groups.
problem Proportion of non-pseudo-Anosov mapping classes in a ball of radius R.
method Using word metric and finite generating sets, we show that the proportion decreases exponentially.
result Proportion of non-pseudo-Anosov mapping classes decreases exponentially.
Study symmetry groups and curves from sums of exponentials.
problem Understanding the geometry and symmetry of curves from sums of exponentials.
method Analysis of symmetry groups, winding numbers, and parametrization of the unit circle.
result Unified method for constructing curves with specific properties.
Motivated by the pricing of lookback options in exponential Lévy models, we study the difference between the continuous and discrete supremum of Lévy processes. In particular, we extend the results of Broadie et al. (1999) to jump-diffusion models. We also derive bounds for general exponential Lévy models.
Normalization layers control deep neural network capacity, improving stability and generalization.
problem Excessive capacity in deep neural networks leads to overfitting and poor generalization.
method Developed a theoretical framework to explain normalization's role in capacity control.
result Normalization layers reduce the Lipschitz constant exponentially, smoothing the loss landscape and enhancing generalization.
Exponentially smoothed RNNs improve industrial forecasting.
problem Complexity and non-stationarity in industrial time series data.
method Exponential smoothed recurrent neural networks (RNNs) for modeling non-linear dynamics.
result Exponentially smoothed RNNs outperform traditional models in multi-step forecasting.
We study tilting subweibull distributions and their tail behavior.
problem Understanding tail behavior of subweibull distributions.
method Alternative characterizations and conditions for tail behavior preservation.
result Conditions for tail behavior preservation after exponential tilting.
This work achieves exponential concentration in heavy-tailed data over CAT(κ) spaces using the Fréchet median.
problem Achieving robust estimation in heavy-tailed data distributions.
method Developing a concentration bound for the Fréchet median in CAT(κ) spaces.
result Exponential concentration of the Fréchet median in CAT(κ) spaces over heavy-tailed data.
Develops a new exponential map for time-varying vector fields.
problem Lack of global flows for general time-varying vector fields.
method Categorical development of spaces of vector fields and flows, allowing for systematic localisation.
result Derives the homeomorphism of the exponential map for vector fields with measurable time-dependence.
We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks …
The study provides error bounds for the generalized Lasso with sub-exponential data.
problem Analyzing the generalized Lasso under sub-exponential data distributions.
method Non-asymptotic analysis using generic chaining-based proof strategy.
result Error bounds for the generalized Lasso can be controlled by two complexity parameters.
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where quantum computer may offer significant speedup. Several quantum algorithms for discr…
New model captures time-varying volatility with stochastic exponential tails.
problem Capturing time-varying volatility and stochastic skewness in financial markets.
method Normal Tempered Stable distribution with time-varying parameter.
result Model better explains market option prices with stochastic exponential tails.
Develops a lifting theory for exponential maps in semi-Riemannian geometry.
problem Overcoming singularities in exponential maps to prove geodesic connectivity.
method Lifting theory for semi-Riemannian manifolds with path-continuation property.
result General path-lifting theorem extending globally under certain conditions.
New Thompson sampling algorithm reduces regret for exponential family bandits.
problem Minimizing regret in multi-armed bandit problems with exponential family rewards.
method Proposes ExpTS and ExpTS+ algorithms using novel sampling distributions. result Minimizes both finite-time and asymptotic regret for exponential family rewards.
Efficient method for learning continuous exponential families beyond Gaussian.
problem Learning continuous exponential families with unbounded support.
method Interaction Screening approach for scalable learning of continuous graphical models.
result Our estimator maintains similar accuracy and sample complexity scalings compared to alternative approaches, while improving run-time.
The goal of this paper is to prove a result conjectured in Föllmer and Schachermayer [FS07], even in slightly more general form. Suppose that S is a continuous semimartingale and satisfies a large deviations estimate; this is a particular growth condition on the mean-variance tradeoff process of S. We show that S then …
We study the exponential map of connected symmetric spaces and characterize, in terms of midpoints and of infinitesimal conditions, when it is a diffeomorphism, generalizing the Dixmier-Saito theorem for solvable Lie groups. We then give a geometric characterization of the (strongly) exponential solvable symmetric spac…
We provide equivalence of numerous no-free-lunch type conditions for financial markets where the asset prices are modeled as exponential Levy processes, under possible convex constraints in the use of investment strategies. The general message is the following: if any kind of free lunch exists in these models it has to…
Study shows exponential error reduction in multiclass classification without bias-variance trade-off.
problem Multiclass classification with margin conditions.
method Analysis of classification error under hard-margin conditions.
result Exponential decrease in classification error without bias-variance trade-off.
This paper analyzes VAE approximation errors in conditional exponential families.
problem Posterior collapse and approximation errors in VAEs.
method Analysis of ELBO objective and conditional exponential families.
result The ELBO optimizer pulls away from the likelihood optimizer towards a consistent subset of models.
Paper proposes SLINK clustering for nonparametric data sequences with improved consistency.
problem Nonparametric clustering of data sequences from unknown distributions.
method Exponentially consistent nonparametric SLINK clustering algorithm.
result SLINK clustering achieves exponential consistency under less strict conditions.
New energy functional and fields for Yang-Mills theory, proving monotonicity and vanishing theorems.
problem Developing new mathematical tools for Yang-Mills theory.
method Introducing normalized exponential Yang-Mills energy functional, deriving monotonicity formula and vanishing theorem.
result Monotonicity and vanishing theorems for exponential Yang-Mills fields.
We investigate a class of quadratic-exponential growth BSDEs with jumps. The quadratic structure introduced by Barrieu & El Karoui (2013) yields the universal bounds on the possible solutions. With local Lipschitz continuity and the so-called A_gamma-condition for the comparison principle to hold, we prove the existenc…
In the setting of exponential investors and uncertainty governed by Brownian motions we first prove the existence of an incomplete equilibrium for a general class of models. We then introduce a tractable class of exponential-quadratic models and prove that the corresponding incomplete equilibrium is characterized by a …
We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first-passage time probability and expected occupation time of sets of a Le…
Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging. For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be acquired and thus how to recover the full signal becomes an active research topic. Bu…
This paper extends exponential smoothing to distributional time series using Wasserstein distance.
problem Forecasting distributional time series with exponential smoothing.
method Generalized exponential smoothing in Wasserstein space, with consistent parameter estimation.
result Wasserstein exponential smoothing outperforms traditional methods in high-frequency financial and electricity demand data.
The paper proposes a method to train time-varying generative models using natural gradients.
problem Training time-varying generative models efficiently and accurately.
method Projecting generative model parameters onto an exponential family manifold and optimizing using natural gradient descent.
result The proposed method efficiently approximates the natural gradient and can be applied to various exponential family models.
This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a sequence of utilities defined on R converges to the exponential utility. Under a …
Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning paradigm is based on the combination of random walks for sampling context nodes and t…
Paper analyzes sparse aggregation in GLMs with Kullback-Leibler risk bounds.
problem Sparse aggregation in GLMs for parameter approximation.
method Exponential weighted aggregation scheme with Kullback-Leibler risk bounds.
result Sharp oracle inequality for Kullback-Leibler risk with leading constant 1 and minimax-optimal rate of aggregation.
Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian distribution. We extend the EPCA model toolbox by presenting the first exponentia…
The paper introduces exponential-wrapped distributions on symmetric spaces for better data modeling.
problem Challenges in statistical modeling due to curvature of data spaces.
method Construction and use of exponential-wrapped distributions on affine locally symmetric spaces.
result Exponential-wrapped distributions on symmetric spaces have useful properties for practical use.
Frame flows on certain symmetric spaces mix exponentially.
problem Exponential mixing of frame flows in convex cocompact locally symmetric spaces.
method Generalized local non-integrability and non-concentration properties to apply Dolgopyat's method.
result Exponential mixing of frame flows proved for convex cocompact locally symmetric spaces.