Conventional research attributes the improvements of generalization ability of deep neural networks either to powerful optimizers or the new network design. Different from them, in this paper, we aim to link the generalization ability of a deep network to optimizing a new objective function. To this end, we propose a \…
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48 results for “Nonlinear objective functions”
Controller seeks informative system observations to predict nonlinear dynamics.
problem Predicting nonlinear dynamics with uncertain parameters.
method Expected free energy minimization for balancing goal state and informative observations.
result Controller improves performance in uncertain parameter scenarios.
New error bounds for GANs with nonlinear objective functions derived.
problem Statistical consistency of GANs with nonlinear objective functions.
method Derivation of statistical error bounds for -GANs using Rademacher complexity.
result Proves the statistical consistency of -GANs.
We show that, locally, all geometric objects of Generalized Kahler Geometry can be derived from a function K, the "generalized Kahler potential''. The metric g and two-form B are determined as nonlinear functions of second derivatives of K. These nonlinearities are shown to arise via a quotient construction from an aux…
Method solves complex optimization problems with high probability bounds.
problem Nonlinear equality constrained stochastic optimization problems.
method Step-search sequential quadratic programming method.
result High-probability bound on iteration complexity for first-order stationarity.
New method reveals true causal functions in nonlinear time series, not just scores.
problem Causal discovery in nonlinear time series often uses scalar edge scores, which hide true function-valued causal influence.
method Formalized function-valued causal influence for additive, contribution-decomposable architectures. Introduced a practical framework based on ICE for estimating causal response functions directly from trained models.
result Edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors.
We propose a method for maximizing a partial area under a receiver operating characteristic (ROC) curve (pAUC) for binary classification tasks. In binary classification tasks, accuracy is the most commonly used as a measure of classifier performance. In some applications such as anomaly detection and diagnostic testing…
New algorithms reduce complexity for solving nonconvex optimization problems with stochastic objectives and constraints.
problem Solving nonconvex optimization problems with stochastic objectives and constraints.
method Single-loop quadratic penalty and augmented Lagrangian algorithms with variance reduction techniques.
result Achieved best-known complexity guarantees for solving nonconvex optimization problems with stochastic objectives and constraints.
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is studied as an example of bundle-like objects with discordant (sogo) transition functi…
New method for separating mixed signals with nonlinear functions.
problem Recovering source signals from nonlinear mixtures.
method Optimisation-based function approximation to minimize mutual statistical dependence.
result The method can recover source signals from nonlinear mixtures under certain conditions.
This work overcomes bias in concave multi-objective reinforcement learning.
problem Gradient bias in policy gradient methods for concave scalarized multi-objective reinforcement learning.
method Developed a Natural Policy Gradient (NPG) algorithm with a multi-level Monte Carlo (MLMC) estimator.
result Achieved optimal sample complexity for computing an -optimal policy.
New algorithm tackles stochastic optimization with inequality constraints.
problem Stochastic optimization with inequality constraints in various applications.
method Active-set stochastic sequential quadratic programming (StoSQP) with a differentiable exact augmented Lagrangian.
result Global convergence for any initialization, KKT residuals converge to zero almost surely.
In this paper we study some geometrical objects (d-tensors, multi-time semisprays of polymomenta and nonlinear connections) on the dual 1-jet vector bundle . Some geometrical formulas, which connect the last two geometrical objects, are also derived. Finally, a canonical nonlinear…
The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the curse of dimensionality by embedding the nonlinear feature space into a low dim…
A new algorithm solves constrained optimization problems with stochastic gradients.
problem Nonlinear equality constrained optimization with rank-deficient Jacobians.
method Step decomposition strategy combining normal and tangential steps.
result Convergence guarantees in rank-deficient Jacobian cases.
Deep nonlinear models pose a challenge for fitting parameters due to lack of knowledge of the hidden layer and the potentially non-affine relation of the initial and observed layers. In the present work we investigate the use of information theoretic measures such as mutual information and Kullback-Leibler (KL) diverge…
Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and their embedding quality can be poor. We propose a natural extension to several …
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results. Coping with the infinite dimensionality and non-convexity of these problems typica…
A Family of Computationally Efficient and Simple Estimators for Unnormalized Statistical Modelscs.LG
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte Carlo estimation of Geyer and Thompson (1992). The family is such that we can e…
A hybrid algorithm combines optimization and enumeration for symbolic regression.
problem Finding any function from a set of operators without prior specification.
method Mixed-integer nonlinear optimization with explicit enumeration and constraints.
result The hybrid algorithm is competitive with state-of-the-art methods.
Develops a new duality between entropy martingale optimal transport and nonlinear pricing-hedging.
problem Entropy Martingale Optimal Transport problem and its associated optimization problem.
method Combines Entropy Optimal Transport and Martingale Optimal Transport theories, with novel penalization terms and constraints.
result Establishes a nonlinear robust pricing-hedging duality, covering various known robust results.
Proposes a new derivative concept for nonlinear DRO problems.
problem Optimizing nonlinear functions in probability space with distributionally robust optimization.
method Introduces Gateaux derivative for smoothness and proposes a Frank-Wolfe algorithm.
result Validates theoretical results on portfolio selection problems with numerical validation.
A novel optimisation framework through quadratic nonlinear projection is introduced for credit portfolio when the portfolio risk is measured by Conditional Value-at-Risk (CVaR). The whole optimisation procedure to search toward the optimal portfolio state is conducted by a series of single-step optimisations under the …
Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. However, BO is practically limited to optimizing 10--20 parameters. To scale BO to high dimensions, we usually make str…
Proposes FunNoL for better curve classification and reconstruction in multivariate functional data.
problem Linear methods fail to capture nonlinear structures in multivariate functional data.
method Functional nonlinear learning (FunNoL) method using nonlinear mapping.
result FunNoL outperforms FPCA in curve classification and reconstruction, especially in multivariate settings.
New methods for functional data analysis improve manifold methods for continuous data.
problem Challenges in evaluating embeddings for functional data.
method Transfer manifold methods from tabular and image data to functional data, define a theoretical framework, and propose nuanced evaluation strategies.
result Manifold methods can be successfully applied to functional data, but careful evaluation is needed.
New algorithm solves stochastic optimization problems with unknown gradients.
problem Solving nonlinear optimization problems with stochastic objectives and deterministic constraints.
method Adaptive SQP with differentiable exact augmented Lagrangian and stochastic line search.
result Global convergence established for both non-adaptive and adaptive SQP methods.
Kernel VICReg improves SSL in RKHS, capturing nonlinear structures.
problem Limited ability of existing SSL methods to handle nonlinear dependencies.
method Kernel VICReg framework in RKHS, kernelizing VICReg objectives.
result Kernel VICReg mitigates representational collapse and improves performance.
Combines Gaussian processes and polynomial chaos for stochastic control.
problem Uncertainties in dynamic models lead to performance issues in predictive control.
method Combines Gaussian processes with polynomial chaos expansions to estimate probability distributions of nonlinear functions.
result Demonstrates accurate approximation and closed-loop performance in stochastic nonlinear model predictive control.
New algorithms solve complex function optimization problems.
problem Optimizing unknown functions in competitive learning models.
method Proposed F-LCB algorithm based on UCB-type methods for nonlinear optimization.
result Regret upper bounds for the F-LCB algorithm derived from base algorithms' convergence rates.
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear coordinate transformations with data-driven methods. Recently, researchers have pro…
Neural network predicts functional responses from scalar inputs.
problem Regression of functional responses with large scalar predictors and nonlinear relationships.
method Transform functional response to finite dimensions, design feed-forward neural network, modify output via objective functions, apply roughness penalty.
result Proposed neural network outperforms conventional methods in multiple scenarios.
Novel algorithm optimizes decision trees for nonlinear metrics.
problem Optimizing decision trees for nonlinear metrics like F1-score.
method Bi-objective optimisation approach to find optimal trees on Pareto frontier.
result The optimal tree for nonlinear metrics lies on the Pareto frontier.
With an eye towards human-centered automation, we contribute to the development of a systematic means to infer features of human decision-making from behavioral data. Motivated by the common use of softmax selection in models of human decision-making, we study the maximum likelihood parameter estimation problem for sof…
Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. In this…
New method for nonlinear SDR of complex non-Euclidean data.
problem Nonlinear SDR for complex non-Euclidean random objects.
method Fréchet Cumulative Covariance (FCCov) and neural networks.
result Robust and unbiased nonlinear SDR for complex data.
The study quantifies how many objects can be linearly classified under all views.
problem Understanding the expressivity of group-equivariant representations.
method Generalization of Cover's Function Counting Theorem to quantify separable dichotomies.
result The fraction of separable dichotomies is determined by the fixed space dimension of the group action.
The paper proposes a new system ID method from noisy data.
problem System identification of linear and nonlinear non-autonomous systems from noisy and sparse data.
method Bayesian formulation for learning a hidden Markov model with stochastic dynamics, analyzed in the context of least squares and multiple shooting approaches.
result The proposed approach outperforms existing methods in terms of mean squared error and model generalizability.
Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding critical points of a quadratic function subject to quadratic constraints. In this paper we show that a certain class of con…
This paper introduces a new method for semi-supervised learning on high dimensional nonlinear manifolds, which includes a phase of unsupervised basis learning and a phase of supervised function learning. The learned bases provide a set of anchor points to form a local coordinate system, such that each data point on…
Survey on a nonlinear d'Alembertian from general relativity.
problem Understanding a new nonlinear operator from relativity.
method Review of a new distributional d'Alembertian, comparison estimates, and exact representation formulas.
result Control of the timelike cut locus through optimal transport.
InfiniteWalk connects deep network embeddings to spectral graph theory with a nonlinear transformation.
problem Learning node representations from networks with deep learning methods.
method Study of the DeepWalk objective in the limit as window size goes to infinity, linking to spectral graph embeddings with a nonlinear transformation.
result Simple binary thresholding of the Laplacian pseudoinverse can approximate DeepWalk embeddings.
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraint violation. …
Bayesian optimization (BO) has been broadly applied to computational expensive problems, but it is still challenging to extend BO to high dimensions. Existing works are usually under strict assumption of an additive or a linear embedding structure for objective functions. This paper directly introduces a supervised dim…
Automated denoising score matching handles nonlinear diffusion processes.
problem Nonlinear diffusion processes limit generative modeling and property estimation.
method Local-DSM using local increments and Taylor expansions.
result Tractable training and score estimation for nonlinear diffusion processes.
Forecasting based on financial time-series is a challenging task since most real-world data exhibits nonstationary property and nonlinear dependencies. In addition, different data modalities often embed different nonlinear relationships which are difficult to capture by human-designed models. To tackle the supervised l…
New method learns optimal policies in presence of unmeasured confounders.
problem Optimal policy learning with unobserved confounders.
method Causal-assisted policy learning methods using instrumental variables and negative controls.
result Policies are quantile-optimal under mild coverage assumptions.
Proposes IIB for domain generalization, overcoming failure modes of IRM.
problem Domain generalization with nonlinear classifiers and pseudo-invariant features.
method Invariant Information Bottleneck (IIB) using mutual information and variational formulation.
result Significantly outperforms IRM on synthetic datasets and real-world benchmarks.