The paper speeds up hyperparameter optimisation in Gaussian processes.
problem Scaling hyperparameter optimisation to large datasets.
method Improvements to linear system solvers (pathwise gradient, warm starting, early stopping).
result Speed-ups of up to 72x and residual norm decreases of up to 7x.
This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be used as a black box to speed up linear programming solvers dramatically, by two…
Exact solver speeds up Weston-Watkins SVM subproblem significantly.
problem Improving performance of Weston-Watkins multiclass SVM.
method Novel reparametrization for exact subproblem solving.
result Significant speed-up over state-of-the-art solvers for large number of classes.
Novel probabilistic solver speeds up solving related linear systems.
problem Efficiently solving multiple related linear systems.
method Probabilistic linear solver over the parameter space, leveraging solved systems.
result Faster and more efficient solution of related linear systems.
New framework for probabilistic linear solvers reduces manual effort.
problem Manual implementation of probabilistic iterative methods is laborious.
method Affine Tracing: Automatically constructs PIMs from standard implementations.
result Any realistic affine PIM is calibrated, motivating their adoption.
Developing stable and scalable probabilistic ODE solvers for stiff and high-dimensional problems.
problem Stiff and high-dimensional ODEs
method Matrix-free update step and iterative re-linearization
result Improved stability and scalability
New solver MPLP++ outperforms existing solvers for dense graph models.
problem Efficiently solving dense, discrete Graphical Models with pairwise potentials.
method Dual Block-Coordinate Ascent with MPLP++ modification.
result MPLP++ significantly outperforms existing solvers, including TRWS.
A learning algorithm optimizes SOR solver parameters for a sequence of linear systems efficiently.
problem Optimizing solver parameters for a sequence of related linear systems without extra computations.
method Bandit and contextual bandit algorithms for online learning of optimal parameters.
result The overall cost approaches the best fixed parameter as the sequence length increases.
Parallel-in-time solver reduces ODE simulation time from linear to logarithmic.
problem Efficiently solving ordinary differential equations (ODEs) with reduced computational cost.
method Formulated a parallel-in-time probabilistic numerical ODE solver using time-parallel formulation of iterated extended Kalman smoothers.
result Reduces span cost from linear to logarithmic in the number of time steps.
New CAGP-GS framework improves Gaussian process uncertainty quantification.
problem Scaling issue in Gaussian processes for large datasets.
method Calibrated probabilistic linear solvers for reduced complexity.
result CAGP-GS framework provides more realistic uncertainty quantification.
Efficient algorithms speed up adversarial training for linear models.
problem Adversarial training for linear models is computationally expensive.
method Tailored optimization algorithms for regression and classification.
result Significantly faster convergence rates for large-scale problems.
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative …
New method uses Gaussian processes to improve PDE solver accuracy.
problem Uncertainty in PDE solver parameters and measurements.
method Physics-informed Gaussian process regression.
result Strictly generalizes weighted residual methods.
Physarum-inspired solver speeds up LP solving in neural networks.
problem Efficiently solving linear programming problems within neural networks.
method Inspired by Physarum dynamics, a differentiable solver for LPs.
result Solver outperforms existing methods in video segmentation and few-shot learning.
Probabilistic solvers improve stability for stiff systems.
problem Performance penalties for small steps in stiff systems.
method Probabilistic exponential integrators that include fast linear dynamics in the prior.
result Proven L-stability and probabilistic error accounting.
This work extends VQR to non-linear cases and provides scalable solvers.
problem Limitations of VQR in handling non-linear relationships and scalability.
method Extension to non-linear VQR, vector monotone rearrangement, fast solvers.
result Substantial improvement over linear VQR and scalable solvers.
SA-Solver improves stochastic sampling from DPMs.
problem Efficient sampling from Diffusion Probabilistic Models (DPMs) is time-consuming.
method Proposes SA-Solver, an improved stochastic Adams method for solving diffusion SDE.
result SA-Solver achieves improved or comparable performance compared to SOTA methods for few-step sampling.
Holistic GLMs add constraints for better model quality.
problem Improving classical linear regression models.
method Sparsity-inducing, sign-coherence, and linear constraints.
result Holistic GLMs reliably solve GLMs for various responses.
AI-driven framework optimizes MCMC-based preconditioners for faster linear system solving.
problem Slow convergence of Krylov subspace solvers for ill-conditioned matrices.
method Graph neural surrogate and Bayesian optimization for AI-tuned MCMC parameters.
result 50% reduction in iterations to convergence on unseen system.
New method solves constrained optimization problems efficiently.
problem Equality-constrained nonlinear, nonconvex optimization problems.
method Adaptive inexact Newton method with randomized iterative sketching.
result Global almost sure convergence and local linear/superlinear convergence.
skscope simplifies sparsity-constrained optimization in Python.
problem Tedious mathematical deduction and programming for sparsity-constrained optimization.
method Introduces skscope, a Python library that allows users to solve sparsity-constrained optimization problems by just programming the objective function.
result skscope enables state-of-the-art solvers to quickly attain sparse solutions in high-dimensional spaces, achieving up to 80x speedup.
MIP-GNN uses graph neural networks to predict variable biases for MIP solvers.
problem Improving combinatorial optimization through data-driven insights.
method Encoding MILP interactions as graphs, training a graph neural network to predict variable biases, and guiding the MIP solver with these predictions.
result Significant improvements in solving binary MILPs compared to default settings of state-of-the-art solvers.
A systematic algorithm for building integrating factors of the form mu(x,y') or mu(y,y') for non-linear second order ODEs is presented. When such an integrating factor exists, the algorithm determines it without solving any differential equations. Examples of ODEs not having point symmetries are shown to be solvable us…
DPM-Solver speeds up DPM sampling to 10-20 function evaluations.
problem Slow sampling from Diffusion Probabilistic Models (DPMs).
method Exact formulation of diffusion ODE solutions, using change-of-variable and exponentially weighted integral.
result Generates high-quality samples in 10-20 function evaluations.
New method calibrates probabilistic linear solver for online coverage guarantees.
problem Uncertainty in probabilistic linear solver solutions without coverage guarantees.
method Online conformal prediction-PLS (OCP-PLS) method to calibrate uncertainty thresholds.
result Validates online calibration of uncertainty thresholds via online conformal prediction.
Neural networks that are based on unfolding of an iterative solver, such as LISTA (learned iterative soft threshold algorithm), are widely used due to their accelerated performance. Nevertheless, as opposed to non-learned solvers, these networks are trained on a certain dictionary, and therefore they are inapplicable f…
In this paper, we present C-ADAM, the first adaptive solver for compositional problems involving a non-linear functional nesting of expected values. We proof that C-ADAM converges to a stationary point in O(δ−2.25) with δ being a precision parameter. Moreover, we demonstrate the importance of our resul…
We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the other to gradient matching. All methods have greater accuracy than previously sugge…
Graph neural networks improve AMG convergence for sparse systems.
problem Efficiently constructing algebraic multigrid prolongation operators for sparse linear systems.
method Train a graph neural network to learn prolongation operators from matrix classes, using an unsupervised loss function.
result Improved convergence rates compared to classical AMG methods.
Paper introduces a new method to solve complex PDEs efficiently.
problem Solving high-dimensional semilinear PDEs and BSDEs.
method Decomposes PDEs into linear and nonlinear parts, uses Deep BSDE solver with control variate method.
result Errors of the new method are much smaller than those of the original Deep BSDE solver.
A new ML method speeds up PDE simulations without needing classical training.
problem Accelerating transient PDE simulations using machine learning.
method Online-learned preconditioners using a bandit algorithm.
result One-shot acceleration of PDE simulations.
Study evaluates Deep PDE solvers for high-dimensional option pricing, identifying key sources of error.
problem Empirical study on error analysis of Deep PDE solvers for high-dimensional option pricing.
method Comparative experiments with Deep BSDE method and other solvers, identifying three main sources of error.
result Deep BSDE method is superior and robust to option specifications, improving with larger batch sizes and fewer time steps.
This paper studies the problem of learning the conditional distribution of a high-dimensional output given an input, where the output and input may belong to two different domains, e.g., the output is a photo image and the input is a sketch image. We solve this problem by cooperative training of a fast thinking initial…
A scalable method for training prediction models in predict-then-optimize
problem Training prediction models in the predict-then-optimize paradigm
method Decision-focused learning pipeline
result Decision quality competitive with state-of-the-art methods while reducing training time
Rex solves the inverse problem for ODE/SDE solvers, improving precision and stability.
problem Inversion of ODE/SDE solvers is inaccurate and impractical for precision applications.
method Rex uses Lawson methods to convert explicit Runge-Kutta schemes into algebraically reversible ones.
result Rex achieves near-machine-precision reconstruction and improves generative models.
SeqRF straightens generative model flows to speed up sampling.
problem High global truncation error in ODE-based solvers for generative models.
method SeqRF, a learning technique that straightens the probability flow.
result Significantly improved sampling speed and synthesis quality.
The use of machine learning algorithms to address classification problems is on the rise in many research areas. The current study is aimed at testing the potential of using such algorithms to auto-select the best solvers for transport problems in uniform slabs. Three solvers are used in this work: Richardson, diffusio…
ASkotch solves large-scale KRR faster and better than existing methods.
problem Challenges in scaling full Kernel Ridge Regression (KRR) to large datasets.
method ASkotch: A scalable, accelerated, iterative method for full KRR.
result ASkotch provides better solutions faster than state-of-the-art solvers for full and inducing points KRR.
Diffusion models tackle noisy inverse problems with posterior sampling.
problem Efficiently solving general noisy inverse problems.
method Approximation of posterior sampling for diffusion models.
result Diffusion models can handle various noise statistics and nonlinear problems.
There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al. introduced a sampling-based class of methods that are 'well-calibrated' in a specific sense. But the computational c…
We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the L1 norm of the feature weights vector and relies on a quantum linear programming solver instead of a classical solver. Sparse SVM leads to sparse models that use only a small fr…
Transformers learn to predict temporal logic solutions from classical solver outputs.
problem Training neural networks on logic problem solutions for verification.
method Training a Transformer on generated training data from classical solvers, focusing on one solution per formula.
result Transformers can predict correct solutions to temporal logic problems, even to unseen benchmarks.
In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the Stochastic Gradient Langevin Dynamics algorithm to draw samples from the posterior …
Develops a new solver for path-dependent PDEs using signature kernels.
problem Solving path-dependent PDEs (PPDEs) efficiently and accurately.
method Uses signature kernels to solve PPDEs by approximating the solution with minimal norm in a reproducing kernel Hilbert space.
result Proves the consistency of the numerical scheme, ensuring convergence to PPDE solutions as the number of collocation points increases.
New LNS framework improves integer program solving.
problem Solving large-scale integer linear programs efficiently.
method Large neighborhood search with imitation and reinforcement learning.
result Framework significantly outperforms commercial solvers.
Achieving fusion of deep learning with combinatorial algorithms promises transformative changes to artificial intelligence. One possible approach is to introduce combinatorial building blocks into neural networks. Such end-to-end architectures have the potential to tackle combinatorial problems on raw input data such a…
New algorithm speeds up sampling from log-concave distributions over polytopes.
problem Sampling from log-concave distributions constrained to polytopes efficiently.
method Improved Markov chain with efficient linear solvers and randomized estimators.
result Per-step complexity is nearly optimal, with reduced arithmetic operations.
RL accelerates portfolio optimization and option pricing by dynamically adjusting preconditioner sizes.
problem Large linear systems in portfolio optimization and option pricing lead to slow convergence.
method Reinforcement Learning (RL) dynamically adjusts block-preconditioner sizes to accelerate convergence.
result RL-driven solver significantly reduces computational cost and accelerates convergence.