Proposes NC-VAE to prevent posterior collapse in VAEs.
problem Posterior collapse in variational autoencoders (VAEs).
method Noise contrastive estimation applied to VAEs.
result Proves NC-VAE cannot reach posterior collapse and provides lower bounds.
Local search heuristics for non-convex optimizations are popular in applied machine learning. However, in general it is hard to guarantee that such algorithms even converge to a local minimum, due to the existence of complicated saddle point structures in high dimensions. Many functions have degenerate saddle points su…
Bayesian optimization has demonstrated impressive success in finding the optimum input x* and output f* = f(x*) = max f(x) of a black-box function f. In some applications, however, the optimum output f* is known in advance and the goal is to find the corresponding optimum input x*. In this paper, we consider a new sett…
RWR converges to global optimum in certain settings.
problem Proving convergence of RWR to optimal policy.
method Iterative learning with return-weighted log-likelihood.
result RWR converges to global optimum under certain conditions.
OPFython simplifies Optimum-Path Forest for Python users.
problem Lack of diversity and complexity in conventional classification algorithms.
method Develops a Python-based Optimum-Path Forest framework.
result OPFython provides a more friendly and faster prototyping environment.
New analysis improves sample complexity for vanilla policy gradient methods.
problem Improving sample complexity guarantees for vanilla policy gradient methods.
method Adapting tools from SGD analysis to policy gradient methods, with smoothness and gradient approximation assumptions.
result Established improved sample complexity bounds for convergence and global optimum.
Mixed membership factorization is a popular approach for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee estimates from a local optimum. Here, we derive a global optimization (GOP) algor…
Noise helps neural networks escape local optima.
problem Understanding the role of noise in neural network training.
method Perturbed gradient descent and noise annealing.
result Noise guarantees convergence to global optimum in polynomial time.
Optimum-statistical collaboration improves black-box optimization efficiency.
problem Improving black-box optimization efficiency through better statistical collaboration.
method Introducing optimum-statistical collaboration framework for hierarchical bandits-based optimization.
result Demonstrated improved regret bounds and better performance in experiments.
Bayesian optimisation is improved by incorporating expert prior through space warping.
problem Cold start phase in expensive function optimisation.
method Prior distribution warps the search space around high probability regions of function optimum.
result Improves optimisation performance through acquisition agnostic approach.
In this paper, a new sequential surrogate-based optimization (SSBO) algorithm is developed, which aims to improve the global search ability and local search efficiency for the global optimization of expensive black-box models. The proposed method involves three basic sub-criteria to infill new samples asynchronously to…
Bayesian Optimization with a Prior for the Optimum (BOPrO) improves efficiency and accuracy.
problem Bayesian Optimization's standard priors are not intuitive for domain experts.
method BOPrO injects expert knowledge into the optimization process using priors about the optimum.
result BOPrO is 6.67x faster than state-of-the-art methods and achieves new state-of-the-art performance.
Novel method for high-dimensional BO using CMA to define local regions.
problem Challenges in applying BO to high-dimensional optimization problems.
method CMA strategy to learn search distribution and define local regions.
result Our method outperforms existing techniques on various benchmarks.
This paper compares three portfolio designs for Indian stocks.
problem Designing an optimum portfolio that balances return and risk.
method Three approaches: minimum risk, optimum risk, and Eigen portfolios.
result Optimum risk portfolios and Eigen portfolios identified for each sector.
Postprocessing reduces Bayesian optimization steps for global optima.
problem Slow convergence in Bayesian optimization for high-dimensional problems.
method Prohibits duplicated samples in the dataset postprocessing method.
result Significantly reduces the number of sequential steps to find the global optimum.
Gradient descent with noise converges to a unique optimum in nonconvex matrix factorization.
problem Gradient descent with noise converges to a unique optimum in nonconvex matrix factorization.
method A perturbed form of gradient descent with arbitrary initialization.
result Gradient descent with noise converges to a unique optimum.
Community detection in graphs has been the subject of many algorithms. Recent methods want to optimize a modularity function which shows a maximum of relationships within communities and found a minimum of inter-community relations. these algorithms are applied to unipartite, multipartite and directed graphs. However, …
New findings on the max margin problem in neural networks.
problem Understanding the max margin problem in neural networks.
method Analyzing gradient flow and max margin problem in linear and ReLU networks.
result The KKT point is not always an optimum of the max margin problem.
Community detection using both graphs and social networks is the focus of many algorithms. Recent methods aimed at optimizing the so-called modularity function proceed by maximizing relations within communities while minimizing inter-community relations. However, given the NP-completeness of the problem, these algorith…
Shortcut connections in ResNet help avoid local optima, leading to efficient training.
problem Understanding why shortcut connections in ResNet lead to efficient training.
method Two-layer non-overlapping convolutional ResNet, gradient descent with proper normalization.
result Gradient descent avoids spurious local optima, converging to a global optimum.
Proves stable degeneration preserves symplectic forms and confirms Kaledin's conjecture.
problem Symplectic singularities and their degenerations.
method Combining volume minimization, deformation theory, and rigidity results.
result Kaledin's conjecture confirmed for symplectic singularities.
Optimizes expensive experiments by incorporating expert knowledge.
problem Expensive experiments require minimizing the number of trials.
method Bayesian optimization with posterior sampling of expert knowledge.
result Demonstrates significant efficiency gains in experiments and hyperparameter tuning.
We prove that the degenerate part of the distributive homology of a multispindle is determined by the normalized homology. In particular, when the multispindle is a quandle Q, the degenerate homology of Q is completely determined by the quandle homology of Q. For this case (and generally for two term homology of …
New algorithms improve likelihood of finding global optima in Bayesian inference.
problem Finding global optima in Bayesian inference is difficult due to nonconvexity.
method Developed two algorithms: consistent Laplace approximation (CLA) and consistent stochastic variational inference (CSVI).
result Both CSVI and CLA improve likelihood of obtaining global optima compared to standard methods.
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singula…
An n-dimensional submanifold X of a projective space P^N (C) is called tangentially degenerate if the rank of its Gauss mapping γ: X ---> G (n, N) satisfies 0 < rank γ< n. The authors systematically study the geometry of tangentially degenerate submanifolds of a projective space PN(C). By means of the foca…
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.
Study degenerate Bianchi transformations for pseudo-spherical submanifolds in 5D space.
problem Characterize three-dimensional pseudo-spherical submanifolds with degenerate Bianchi transformations.
method Complete description through holonomically degenerate Bianchi transformations.
result Obtained a complete description of degenerate pseudo-spherical submanifolds.
New stabilization found in planar elasticae with degenerate diffusion.
problem Existence of local minimizers in degenerate p-elasticae. method Analysis of pinned planar p-elasticae with degenerate diffusion. result Uncountably many local minimizers with diverging energy in degenerate regime.
Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum. The reason for the absence of probabilistic global optimizers is that the corres…
A new framework for performative prediction robust to distributional misspecification.
problem Performative prediction models can be influenced by their own predictions, leading to suboptimal outcomes.
method Introduces distributionally robust performative prediction (DRPO) to approximate the true performative optimum (PO) robustly.
result DRPO provides provable guarantees as a robust approximation to the true PO when the nominal distribution map is misspecified.
Uniform estimates for Calabi-Yau degenerations proved.
problem Calabi-Yau degenerations of polarised algebraic manifolds.
method Uniform Skoda and L∞-estimates for Kähler potentials. result Uniform Skoda type estimate and L∞-estimate for Calabi-Yau Kähler potentials proved. Sharp diameter bounds for Calabi-Yau degenerations proved.
problem Bounding the diameter of Calabi-Yau metrics during degeneration.
method Sharp upper and lower bounds derived for Ricci-flat Kahler metrics.
result Conjecture confirmed by obtaining precise diameter bounds.
Paper solves degenerated circle pattern metric problem in spherical geometry.
problem Existence and rigidity of (degenerated) circle pattern metrics with prescribed total geodesic curvatures.
method Defined prescribed combinatorial Ricci flows and studied their convergence.
result First degenerated result for total geodesic curvatures in spherical background geometry.
Paper studies degenerated circle packings in hyperbolic geometry and finds conditions for their existence.
problem Whether a prescribed total geodesic curvature can be realized by a degenerated circle packing.
method Introduced combinatorial Ricci flow to find the desired degenerated circle packed surface, analogous to Chow-Luo and Takatsu methods.
result Fully characterized sufficient and necessary conditions for the existence of degenerated circle packings and showed their uniqueness.
Proves unique degeneration of log Fano fibration germs.
problem Stable degeneration of log Fano fibration germs.
method Introduced the H-invariant for filtrations over log Fano fibration germs and used a unique quasi-monomial valuation to achieve the degeneration.
result Unique K-polystable special degeneration of log Fano fibration germs.
This paper analyzes popular time-nonseparable utility functions that describe "habit formation" consumer preferences comparing current consumption with the time averaged past consumption of the same individual and "catching up with the Joneses" (CuJ) models comparing individual consumption with a cross-sectional averag…
New insights on solutions to Allen-Cahn equation with degenerate minimal hypersurfaces.
problem Existence and rigidity of solutions to the Allen-Cahn equation.
method Analysis of degenerate minimal hypersurfaces as limit interfaces.
result New observations and examples of solutions to the Allen-Cahn equation.
Identifies filtration in Lagrangian fibrations to monodromy weight filtration in degenerations.
problem Understanding the relationship between Lagrangian fibrations and degenerations of hyper-Kähler manifolds.
method Identifies and compares perverse filtration with monodromy weight filtration.
result Identifies the perverse filtration of a Lagrangian fibration with the monodromy weight filtration of a degeneration.
Degenerate solutions found in 2D H-system bubbles with higher degrees.
problem Existence of degenerate solutions in H-system bubbles with degree ≥ 3.
method Algebraic characterization of degenerate bubbles.
result Degenerate solutions can exist for H-system bubbles with degree ≥ 3.
We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep network is expressed using a highly non-convex finite-dimensional model, and thus th…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over d-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the sample is drawn i.i.d. from the input distribution, the least squares solution for…
In this paper we study lightlike surfaces of Minkowski 3- space such that they have degenerate or non-degenerate planar normal sections. We first show that every lightlike surface of Minkowski 3− space has degenerate planar normal sections. Then we study lightlike surfaces with non-degenerate planar normal sections a…
Proposes qPO, a new acquisition strategy for batched Bayesian optimization that maximizes the probability of including the optimum.
problem Efficiently identifying top-performing compounds from a large chemical library.
method qPO (multipoint Probability of Optimality) acquisition strategy that maximizes the probability of including the true optimum.
result Empirical evidence shows that qPO is competitive with and complements other state-of-the-art methods in batched Bayesian optimization.
Study metric perturbations to make degenerate harmonic forms non-degenerate.
problem Dealing with degenerate harmonic 1-forms in Riemannian geometry.
method Combining analysis of local expansions with Nash-Moser implicit function theorem.
result Proves deformation to nearby non-degenerate Z/2-harmonic 1-forms.
Study higher rank inner products and their tilings to describe tori degenerations.
problem Understanding metric degenerations of tori.
method Introduce higher rank inner products and their tilings, use to describe degenerations.
result Describe metric degenerations of polarized tori and Hausdorff limits of tilings.
Exact causal network discovery is polynomial for sparse networks.
problem Finding the optimal causal Bayesian network from data is computationally hard.
method Pruning the search space using network properties, combined with dynamic programming and shortest-path searches.
result Exact discovery is polynomial for sparse causal Bayesian networks.
Study real semi-stable degenerations and describe real loci via blow-ups.
problem Describe the homeomorphism type of real loci in degenerations.
method Use real-oriented blow-ups to describe the homeomorphism type of real loci.
result Give more explicit descriptions of real loci as stratified spaces.