Continuous MDS embeds sequences of dissimilarities in Euclidean space.
problem Embedding sequences of dissimilarities as n increases. method Continuous MDS reformulates MDS for sequences of dissimilarity matrices.
result Uniform convergence of interpolated embeddings.
Quantizing large Neural Networks (NN) while maintaining the performance is highly desirable for resource-limited devices due to reduced memory and time complexity. It is usually formulated as a constrained optimization problem and optimized via a modified version of gradient descent. In this work, by interpreting the c…
LSS learns molecular trajectories from MD data.
problem Limited integration time steps in MD simulations.
method Three deep learning networks for slow collective variables, dynamics, and configuration reconstruction.
result Generates ultra-long synthetic folding trajectories.
We present a hybrid continuum-atomistic scheme which combines molecular dynamics (MD) simulations with on-the-fly machine learning techniques for the accurate and efficient prediction of multiscale fluidic systems. By using a Gaussian process as a surrogate model for the computationally expensive MD simulations, we use…
This paper reviews MDS, Sammon mapping, and Isomap, explaining their theory and applications.
problem Exploring multidimensional data structures and mappings.
method Explains classical MDS, metric MDS, kernel classical MDS, Sammon mapping, Isomap, and their applications.
result Detailed understanding of MDS, Sammon mapping, and Isomap methods.
Neuc-MDS extends MDS for non-Euclidean data.
problem Limitations of classical MDS with non-Euclidean data.
method Generalizes inner product to symmetric bilinear forms, optimizes eigenvalues of dissimilarity Gram matrix.
result Optimizes STRESS for non-Euclidean data.
Molecular Dynamics (MD) simulation is widely used to analyze the properties of molecules and materials. Most practical applications, such as comparison with experimental measurements, designing drug molecules, or optimizing materials, rely on statistical quantities, which may be prohibitively expensive to compute from …
New method uses biased MD to create accurate MLIPs.
problem Creating a comprehensive data set for MLIPs.
method Bias MD by MLIP's energy uncertainty, using gradient-based uncertainties.
result Develops uniformly accurate MLIPs with lower computational cost.
The cognitive framework of conceptual spaces proposes to represent concepts as regions in psychological similarity spaces. These similarity spaces are typically obtained through multidimensional scaling (MDS), which converts human dissimilarity ratings for a fixed set of stimuli into a spatial representation. One can d…
JAX MD enables differentiable physics simulations for molecular dynamics.
problem Performing efficient and differentiable physics simulations for molecular dynamics.
method Differentiable physics simulation environments, interaction potentials, neural networks, flexible primitives.
result Differentiable physics simulations can be used for meta-optimization and scaling to large particle systems.
One aim of data mining is the identification of interesting structures in data. For better analytical results, the basic properties of an empirical distribution, such as skewness and eventual clipping, i.e. hard limits in value ranges, need to be assessed. Of particular interest is the question of whether the data orig…
Paper proves MDS NP-hard and provides a PTAS.
problem Theoretical limitations of MDS objective function.
method Proves NP-hardness and provides a PTAS approximation algorithm.
result Minimizing Kamada-Kawai objective is NP-hard.
MD-CGAN models forecast time series with probabilistic posterior distributions.
problem Limited applications of GANs in time series forecasting, especially with probabilistic predictions.
method Mixture Density Conditional Generative Adversarial Model (MD-CGAN) using Gaussian mixture output.
result MD-CGAN outperforms benchmarks, especially in noisy time series.
Timewarp accelerates molecular dynamics by learning to simulate long timescales.
problem Efficiently simulating long timescales in molecular dynamics.
method Uses a normalizing flow to learn large time steps in Markov chain Monte Carlo.
result Generalizes to unseen small peptides, accelerating sampling.
New MD algorithms using Tempesta logarithms for machine learning.
problem Optimization in machine learning with tailored hyperparameters.
method Developed Mirror Descent algorithms using Tempesta multi-parametric logarithms.
result Wide and flexible family of Mirror Descent and mirror-less updates.
MD-GAN learns long-time molecular behavior from short-time data with multi-particle input.
problem Accurately predicting long-time molecular dynamics from short-time data.
method Machine learning method (MD-GAN) that incorporates dynamics of multiple particles of molecules.
result Predicting diffusion with one-third of the training data length using multi-particle input.
New algorithm for reinforcement learning reduces complexity and guarantees convergence.
problem Reinforcement learning problems with convex occupancy measures.
method MD-CURL, inspired by mirror descent, uses non-standard regularization.
result Achieves convergence guarantees and simple closed-form solution.
This paper improves MDS visualization by adjusting Wasserstein distances for heavy-tailed data.
problem Enhancing Multidimensional Scaling (MDS) for better pattern recognition with heavy-tailed distributions.
method Introduces Max-D-SW, a metric adjustment of Max-Sliced Wasserstein distance that aggregates over orthonormal bases.
result Max-D-SW provides a clear numerical advantage in MDS outcomes, especially for heavy-tailed distributions.
There are well-known monomorphisms between the Artin groups of finite type $\arA_n$, $\arB_n=\arC_n$ and affine type $\tilde \arA_{n-1}$, $\tilde\arC_{n-1}$. The Artin group $A(\arA_n)$ is isomorphic to the (n+1)-strand braid group Bn+1, and the other three Artin groups are isomorphic to some subgroups of $B_{n+…
Paper shows equivalence between two alignment methods and introduces a new algorithm.
problem Ensuring human alignment of large language models for useful, safe, and pleasant user experience.
method Introduces IPO-MD algorithm, showing equivalence between IPO and Nash-MD methods.
result Equivalence between IPO and Nash-MD methods proven when considering online version of IPO.
New bounds show linear predictors rarely overfit with certain optimization methods.
problem Bounding test error for linear predictors with stochastic optimization methods.
method Coupling argument for fixed point methods like stochastic and batch mirror descent.
result Locally-adapted rates that depend on predictor properties, not global problem structure.
Paper introduces md-vtrees for efficient probabilistic and causal inference.
problem Efficient inference in complex probabilistic models.
method Introduces md-vtrees to generalize tractability conditions for advanced inference queries.
result Derives first polytime algorithms for causal inference queries.
MDS selects assets by combining daily returns and intraday risk curves, improving portfolio performance.
problem High estimation error in large-scale asset selection.
method Metric Dependence Screening (MDS) incorporating high frequency information as object valued data.
result MDS improves portfolio performance over benchmarks by preserving intraday risk dynamics.
This paper evaluates t-SNE and MDS for reducing dimensions in datasets and classifying them with KNN, ENN, and SVM.
problem Reducing dimensions in datasets for better classification performance.
method t-SNE and MDS applied to nine datasets, followed by KNN, ENN, and SVM classification.
result Performance comparison of t-SNE and MDS with KNN, ENN, and SVM.
Bayesian hyperbolic MDS improves tree-like data representation.
problem Representing tree-like structures in high-dimensional data.
method Bayesian approach to hyperbolic MDS for low-dimensional manifold.
result Bayesian hyperbolic MDS reduces computational complexity and improves accuracy.
Background: Fluctuating hearing loss is characteristic of Meniere's Disease (MD) during acute episodes. However, no reliable audiometric hallmarks are available for counselling the hearing recovery possibility. Aims/Objectives: To find parameters for predicting MD hearing outcomes. Material and Methods: We applied mach…
A new training method improves MLIPs for faster, lighter simulations.
problem High computational and memory costs of complex MLIPs for large-scale MD simulations.
method Teacher-student training framework using latent atomic energy knowledge.
result Lightweight student MLIPs achieve faster MD speeds and comparable accuracy to teachers.
Paper proposes conditional multidimensional scaling for better data reduction.
problem Mapping high-dimensional data to low-dimensional space with known features.
method Developed a broad class of methods called conditional multidimensional scaling (MDS) with an optimization algorithm.
result Conditional MDS improves estimation quality and simplifies visualization and knowledge discovery.
A recent technical breakthrough in the domain of machine learning is the discovery and the multiple applications of Generative Adversarial Networks (GANs). Those generative models are computationally demanding, as a GAN is composed of two deep neural networks, and because it trains on large datasets. A GAN is generally…
MD tree diagnoses model failures using loss landscape metrics.
problem Diagnose model failures without knowing training configuration.
method MD tree based on loss landscape metrics.
result MD tree achieves 87.7% accuracy in dataset transfer tasks, outperforming validation-based approaches.
We present a novel view of nonlinear manifold learning using derivative-free optimization techniques. Specifically, we propose an extension of the classical multi-dimensional scaling (MDS) method, where instead of performing gradient descent, we sample and evaluate possible "moves" in a sphere of fixed radius for each …
Mirror descent method improved RL algorithms.
problem Improving RL algorithms for better performance.
method Mirror descent method applied to RL, solving trust-region problems.
result MDPO outperforms or matches other RL algorithms in continuous control tasks.
Multidimensional scaling (MDS) is a class of projective algorithms traditionally used in Euclidean space to produce two- or three-dimensional visualizations of datasets of multidimensional points or point distances. More recently however, several authors have pointed out that for certain datasets, hyperbolic target spa…
A new method optimizes material discovery by balancing exploration and exploitation.
problem Substantial experimental costs and lengthy development periods in material discovery.
method Threshold-Driven UCB-EI Bayesian Optimization (TDUE-BO) method.
result TDUE-BO significantly outperforms traditional BO methods in material discovery.
Leveraging the intrinsic symmetries in data for clear and efficient analysis is an important theme in signal processing and other data-driven sciences. A basic example of this is the ubiquity of the discrete Fourier transform which arises from translational symmetry (i.e. time-delay/phase-shift). Particularly important…
We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional noisy data. Our method, Minimum Distance Lasso (MD-Lasso), combines minimum distanc…
Extends results of math-ph/0407067
Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over Dirichlet parameters complicate the joint distribution of model parameters. This paper s…
New models reduce discrimination in machine learning without sacrificing explanatory bias.
problem Discrimination and explanatory bias in fairness measures.
method Causal effect estimators using propensity score analysis.
result Theoretical and practical superiority of FairCEEs over existing models.
Extends results of math-ph/0407067
Recent developments in specialized computer hardware have greatly accelerated atomic level Molecular Dynamics (MD) simulations. A single GPU-attached cluster is capable of producing microsecond-length trajectories in reasonable amounts of time. Multiple protein states and a large number of microstates associated with f…
MD-split+ creates locally valid prediction regions for complex data.
problem Localized prediction regions for complex data.
method Localized model performance-based partitioning of feature space X.
result MD-split+ creates valid prediction regions that scale to high dimensions.
Gaining a better understanding of how and what machine learning systems learn is important to increase confidence in their decisions and catalyze further research. In this paper, we analyze the predictions made by a specific type of recurrent neural network, mixture density RNNs (MD-RNNs). These networks learn to model…
Diffusion models simulate molecular dynamics with adjustable accuracy.
problem Simulating molecular dynamics with high accuracy and efficiency.
method Diffusion models as Euler-Maruyama integrators for Langevin dynamics, learning forces from static snapshots.
result Diffusion models generate molecular trajectories with temporal correlations similar to MD simulations.
NeuralMD accelerates protein-ligand binding simulations 1Kx faster.
problem Accurate and efficient simulation of protein-ligand binding dynamics.
method Physics-informed multi-grained group symmetric framework with BindingNet and augmented neural differential equation solver.
result Achieves over 1Kx speedup and up to 15x reduction in reconstruction error compared to standard methods.
Novel deep learning method predicts reaction coordinates and future MD trajectories.
problem Identifying optimal reaction coordinates for chemical reactions.
method Regularized Sparse Autoencoder (RSE) for discovering reaction coordinates and predicting MD trajectory evolution.
result RSE helps in choosing a small but important set of reaction coordinates.
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.
New algorithm for MDS with quasi-polynomial dependency on aspect ratio.
problem Finding an embedding that minimizes a specific objective function for given dissimilarities.
method A novel geometry-aware analysis of a conditional rounding of the Sherali-Adams LP hierarchy.
result Achieved a solution with cost \(O(\log Δ) \cdot extrm{OPT}^{Ω(1)} + ε\) in quasi-polynomial time.