New optimal prior avoids bias in complex models with limited data.
problem Bias in inference from limited data using Jeffreys prior.
method Developed a principled choice of measure that avoids bias, dependent on data quantity.
result Optimal prior leads to unbiased inference in complex models.
We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by …
Study on the limits of learning HMM parameters under various conditions.
problem Understanding the conditions under which hidden Markov model parameters can be learned.
method Nonasymptotic minimax upper and lower bounds, thresholds analysis.
result Nonasymptotic minimax bounds match up to constants, showing learnable thresholds.
Paper estimates Hurst parameter from implied volatilities.
problem Estimating Hurst parameter from implied volatilities.
method Uses covariance between asset return and realized volatility, and applies limit theorems for stochastic volatility models.
result Direct relation between covariance and slope of at-the-money implied volatility established.
We define a stochastic model of a two-sided limit order book in terms of its key quantities \textit{best bid [ask] price} and the \textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps the expected volume rate over the considered price interval invariant, we prove a…
Extended model ensures long-term survival of traders in limited stock market participation.
problem Limited stock market participation and survival of traders over long periods.
method Extended Basak and Cuoco (1998) model with different time-preference coefficients.
result Parameter restrictions ensure long-term survival of traders.
New method uses Gaussian process for limited-data CT reconstruction.
problem Reconstructing internal structures from limited x-ray projections.
method Gaussian process with basis function expansion for parameter estimation.
result Less sensitive to streak artifacts compared to filtered backprojection.
New method improves signal reconstruction with nonconvex penalties and parameter control.
problem Reconstructing sparse signals with nonconvex penalties and nonconvexity control.
method Introduces nonconvex penalties (SCAD, MCP) with nonconvexity parameters and controls them to guide AMP trajectory.
result Achieves perfect reconstruction for relatively dense signals with small nonconvexity parameters.
New phases identified in neural scaling laws with compute limits.
problem Understanding neural scaling laws under compute constraints.
method Solved neural scaling model with stochastic gradient descent, derived loss curves, analyzed model-parameter-count phases.
result Identified 4 phases (+3 subphases) in data-complexity/target-complexity phase-plane, derived exponents.
Study derives a limit functional for Willmore graphs with curvature penalization.
problem Optimizing Willmore graphs with curvature constraints.
method Interpreting penalization as Lagrange multiplier, deriving Γ-limit. result Derives a new limit functional for Willmore graphs.
Mean field Gaussian inference limits mutual information to regularize neural networks.
problem Understanding and quantifying the regularization effect of mean field Gaussian inference.
method Empirically observed and theoretically quantified mutual information limitation through noise.
result Bounding mutual information between parameters and data effectively regularizes neural networks.
A new neural network for text classification reduces parameters with improved accuracy.
problem Reducing the number of parameters in text classification models.
method Compositional coding, capsule network, k-means routing algorithm.
result The proposed method achieves competitive accuracy with significantly fewer parameters.
Study of spectral properties of graph Laplacians for data clustering.
problem Understanding the spectral gap of graph Laplacians for data clustering.
method Analysis of a three-parameter family of differential operators as the large data limit of graph Laplacians.
result The spectral gap depends on three parameters and the size of the perturbation from perfectly clustered data.
A new method sparsifies neural networks by reducing sensitive parameters to zero.
problem Challenges of memory-limited applications due to large number of neural network parameters.
method Quantifies output sensitivity, introduces a regularization term to gradually reduce sensitive parameters.
result Surpasses most recent techniques in sparsity and error rates, achieving twice the sparsity at equal error rates in some cases.
The paper establishes a central limit theorem for estimating the influence parameter in a partially observed Hawkes process system.
problem Estimating the influence parameter in a partially observed Hawkes process system.
method Central limit theorem applied to an estimator of the influence parameter in a partially observed system of Hawkes processes.
result Establishes a central limit theorem for the estimator of the influence parameter under the subcritical condition.
PathCapsNet improves CapsNet by reducing parameters and enhancing performance.
problem Limitations of CapsNet, including excessive parameters and shallow architecture.
method Introducing a deep parallel multi-path version of CapsNet, incorporating depth, max-pooling, regularization, and new routing techniques.
result Better or comparable results to CapsNet with significantly reduced parameter count.
Subjective expected utility theory assumes that decision-makers possess unlimited computational resources to reason about their choices; however, virtually all decisions in everyday life are made under resource constraints - i.e. decision-makers are bounded in their rationality. Here we experimentally tested the predic…
In this paper we construct a compactification for the parameter space of convex projective structures on a fixed n-manifold M. This parameter space is a closed semi-algebraic subset of the variety of characters of representations of the fundamental group of M in SL_{n+1}(R). The boundary is the inverse limit of an inve…
ALFI improves likelihood-free inference for black-box generators.
problem Limitations of likelihood-free inference on black-box generators.
method Adversarial Likelihood-Free Inference (ALFI) to estimate posterior distributions.
result ALFI achieves best parameter estimation accuracy with limited simulation.
Paper develops a method to construct confidence regions for model parameters using batch means method.
problem Constructing confidence regions for model parameters in stochastic gradient descent.
method Batch means method to cancel out covariance matrix, using Polyak-Ruppert averaging.
result Established process-level functional central limit theorem for stochastic gradient descent estimators.
In this paper we introduce a completely continuous and time-variate model of the evolution of market limit orders based on the existence, uniqueness, and regularity of the solutions to a type of stochastic partial differential equations obtained in Zheng and Sowers (2012). In contrary to several models proposed and res…
We construct two one-parameter families of minimal properly embedded surfaces in the Lie group Sol3 using a Weierstrass-type representation. These surfaces are not invariant by a one-parameter group of ambient isometries. The first one can be viewed as a family of helicoids, and the second one is a family of minimal an…
In this paper, we give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps. The quantity of interest is defined as the integrated value over time of the parameter process Θ=T−1∫0Tθt∗dt. We provide a local parametric estimator (LPE) of Θ and conditions u…
A new heuristic for learning Markov network structure efficiently.
problem Complications in learning Markov networks, especially intractable computations and large parameter space.
method A computationally tractable greedy heuristic to limit the number of parameters.
result The method performs comparably well to state-of-the-art methods on real datasets.
At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network functio…
PINNs solve neuronal parameter and state estimation problems with limited data.
problem Estimating parameters and hidden state variables from noisy partial data in multiscale neuronal models.
method Physics-informed neural networks (PINNs) for joint state and parameter estimation.
result PINNs deliver robust and accurate parameter inference and state reconstruction, even with limited data.
Study of conformal limits in Nakajima quiver varieties.
problem Understanding the conformal limits of Nakajima quiver varieties.
method Defined and studied a conformal limit construction for Nakajima quiver varieties, proving it is a limit of a one-parameter family and gives a biholomorphic map.
result Proved the conformal limit is a biholomorphic map between Lagrangian submanifolds of different quiver varieties.
Diffusion means converge to extrinsic means for long times on spheres.
problem Understanding the long-time behavior of diffusion means on manifolds.
method Introduced diffusion means as a parameterized family of location statistics on manifolds, and analyzed their convergence to extrinsic means for long times.
result For real projective spaces and connected compact symmetric spaces, the long-time limit of diffusion means is conjectured to be the extrinsic mean in the isometric embedding.
New method uses KL-divergence to create non-informative priors for multivariate Gaussian.
problem Handling hyperparameters for non-informative limits in multivariate Gaussian conjugate priors.
method Using scaled KL-divergence between multivariate Gaussians to construct Wishart and normal-Wishart conjugate priors.
result Forming non-informative priors without violating Wishart shape parameter restrictions.
New method improves uncertainty quantification in latent variable models.
problem Uncertainty quantification in latent variable models with SGLD-Gibbs.
method Statistical scaling limit theory for SGLD-Gibbs, proposing hyperparameter tuning.
result Explicit guidance on hyperparameter tuning for SGLD-Gibbs ensures meaningful uncertainty quantification.
The intrinsic geometry of the Kerr ergosurface on constant Boyer-Lindquist (BL), Kerr, and Doran time slices is characterized. Unlike the BL slice, which had been previously studied, the other slices (i) do not have conical singularities at the poles (except the Doran slice in the extremal limit), (ii) have finite pola…
Inference in general Ising models is difficult, due to high treewidth making tree-based algorithms intractable. Moreover, when interactions are strong, Gibbs sampling may take exponential time to converge to the stationary distribution. We present an algorithm to project Ising model parameters onto a parameter set that…
Study optimizes sensor placement for accurate parameter estimation in complex systems.
problem Challenges in parameter estimation with limited or noisy data.
method Physics-Informed Neural Networks (PINNs) for optimal sensor placement and parameter estimation.
result PINNs-based framework achieves higher accuracy in parameter estimation compared to random sensor placements.
TM-VI uses flexible transformation models to approximate complex posteriors in Bayesian models.
problem Approximating complex posteriors in Bayesian models with limited flexibility.
method Transformation models for variational inference (TM-VI).
result TM-VI allows accurate approximation of complex posteriors in models with one parameter and works in a mean-field fashion for multi-parameter models.
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from…
Kernelized Support Vector Machines (SVMs) are among the best performing supervised learning methods. But for optimal predictive performance, time-consuming parameter tuning is crucial, which impedes application. To tackle this problem, the classic model selection procedure based on grid-search and cross-validation was …
The study examines Fisher-Riemann geodesics for nonparametric probability densities.
problem Understanding nonparametric probability densities using Fisher-Riemann geometry.
method Obtaining Fisher-Riemann geodesics as a limit of parametric cases with increasing parameters.
result The weak limit approach for nonparametric probability densities.
Gradient descent dynamics in wide neural networks are analyzed using a dynamical CLT.
problem Understanding the fluctuations in wide shallow neural networks trained via gradient descent.
method Dynamical Central Limit Theorem (CLT) applied to neural network dynamics.
result Asymptotic fluctuations remain bounded in mean square throughout training.
We model a closed economic system with interactions that generates the features of empirical wealth distribution across all wealth brackets, namely a Gibbsian trend in the lower and middle wealth range and a Pareto trend in the higher range, by simply limiting the an agents' interaction to only agents with nearly the s…
Bayesian transfer learning improves predictive performance with limited source data.
problem Improving statistical procedures with limited target and source datasets.
method Total risk prior for joint parameter distribution, Bayesian Lasso, model averaging, Gibbs sampling.
result Superior predictive performance compared to frequentist baseline, especially with limited source data.
TensorGuide improves LoRA efficiency and expressivity through joint tensor-train optimization.
problem Limited expressivity and generalization of standard LoRA.
method TensorGuide uses a unified tensor-train structure with controlled Gaussian noise to generate correlated low-rank matrices.
result TensorGuide achieves superior accuracy and scalability with fewer parameters compared to standard LoRA and TT-LoRA.
Computational limitations require more model parameters for robust learning.
problem Computational constraints affect the number of parameters needed for robust learning.
method Analyzes computational limitations and their impact on model size for robust learning.
result Computational bounded learners need significantly more parameters for robust learning.
Let n≥3 and m=n+2n−2. We construct 5-parameters, 4-parameters, 3-parameters ancient solutions of the equation vt=(vm)xx+v−vm, v>0, in R×(−∞,T) for some T∈R. This equation arises in the study of Yamabe flow. We obtain various properties of the ancient so…
We investigate variations of Brieskorn lattices over non-compact parameter spaces, and discuss the corresponding limit objects on the boundary divisor. We study the associated variation of twistors and the corresponding limit mixed twistor structures. We construct a compact classifying space for regular singular Briesk…
Infinitely deep neural networks can be modeled as diffusion processes to avoid undesirable properties.
problem Desirable properties are lost as neural networks increase in depth.
method Parameter distributions shrink as depth increases, leading to well-behaved stochastic processes.
result Limiting processes do not suffer from vanishing dependency and restrictive function families issues.
EPD method accurately captures parameter distributions from RCS data.
problem Limitations of traditional methods in estimating parameter distributions from RCS data.
method EPD method generates synthetic trajectories, estimates parameters, and selects parameters based on discrepancy.
result EPD provides accurate distribution of parameters without data loss.
We analyze operational risk in terms of a spin glass model. Several regimes are investigated, as a functions of the parameters that characterize the dynamics. The system is found to be robust against variations of these parameters. We unveil the presence of limit cycles and scrutinize the features of the asymptotic sta…
Develops 2-categorical methods for multi-parameter persistence.
problem Fundamental limitations of traditional persistence modules.
method 2-categorical structures to capture hierarchical interactions.
result New invariants effectively characterize multidimensional topological features.