This study compares MC and QMC methods for likelihood functions.
problem Approximating the normalizing constant of posterior distributions and marginal likelihoods.
method Characterizes the integration error of MC and QMC methods for likelihood functions.
result QMC outperforms MC under certain conditions, especially in high dimensions.
RQMC improves kernel-based learning by reducing deterministic error and offering computational advantages.
problem Improving kernel-based learning methods to reduce deterministic error and computational complexity.
method Randomized quasi-Monte Carlo (RQMC) methods applied to random feature approximations.
result RQMC methods improve deterministic approximation error bound from O P ( 1 / M ) O_P(1/\sqrt{M}) O P ( 1/ M ) to O ( 1 / M ) O(1/M) O ( 1/ M ) , matching QMC methods. New algorithms solve large-scale rank minimization problems efficiently.
problem Large-scale rank minimization problems.
method Define and apply bi-trace and tri-trace norms to rank minimization problems; design efficient linearized alternating minimization algorithms.
result Proved algorithms converge to critical points; provide RSC and MC error bounds.
A new estimator combines bootstrapping and rollout methods in RL.
problem Combining strengths of bootstrapping and rollout methods in RL.
method Subgraph Bellman operators and fixed point solving.
result Upper bound on error approaches optimal TD variance with additional term.
RQMC improves QMC by providing practical error bounds for financial applications.
problem Lack of practical error estimates in QMC methods.
method Combines Sobol LDS with randomized scrambling methods.
result RQMC outperforms standard QMC in convergence rates and provides error bounds.
Monte Carlo (MC) sampling algorithms are an extremely widely-used technique to estimate expectations of functions f(x), especially in high dimensions. Control variates are a very powerful technique to reduce the error of such estimates, but in their conventional form rely on having an accurate approximation of f, a pri…
New methods for estimating nested expectations in machine learning.
problem Nested expectations in machine learning and statistics.
method Investigation and analysis of statistical implications of nesting Monte Carlo estimators.
result Established conditions for convergence of nested MC estimators and derived corresponding rates.
Adaptive TD learning reduces bias in policy evaluation by switching between TD and MC methods.
problem Achieving accurate policy evaluation with Temporal Difference (TD) learning in the presence of state-specific uncertainty.
method Adaptive switching between TD and Monte Carlo (MC) methods, using learned confidence intervals to detect and mitigate bias.
result The proposed adaptive algorithm outperforms existing methods in policy evaluation tasks.
Posterior refinement improves sample efficiency in Bayesian neural networks.
problem Bayesian neural networks suffer from poor predictive performance due to inaccurate posterior approximations.
method Propose refining Gaussian approximate posteriors with normalizing flows to improve predictive distributions.
result Posterior refinement yields competitive predictive performance with minimal computational overhead.
Paper tackles clipped matrix recovery from scientific areas with theoretical and practical methods.
problem Recovering low-rank matrices from clipped observations in scientific areas.
method Trace-norm minimization algorithm and squared hinge loss with a novel regularization term.
result Theoretical guarantee and practical algorithms for exact recovery of clipped matrix completion.
A new estimator improves efficiency of MC algorithms.
problem Efficiency of Markov chain algorithms.
method Markov chain importance sampling (MCIS).
result Improves error per CPU cycle, often significantly.
The paper models earthquake frequency-magnitude distribution using asymmetric Laplace mixture models.
problem Describing the complete earthquake frequency-magnitude distribution above a completeness magnitude.
method Proposes an asymmetric Laplace mixture model (GFMD-ALMM) to estimate parameters and retrieve mc distribution.
result GFMD-ALMM can accurately model different FMD shapes in various catalogues and sequences.
New sampling strategy improves TR algorithms for stochastic optimization.
problem Derivative-free stochastic optimization with Monte Carlo estimates.
method Stratified adaptive sampling to optimize MC sample size.
result Reduced sample complexity and superior efficiency confirmed.
This paper analyzes stability and generalization of Markov chain stochastic gradient methods.
problem Analyzing stability and generalization of Markov chain stochastic gradient methods.
method Algorithmic stability in statistical learning theory.
result Established optimal generalization bounds for both smooth and non-smooth cases.
Learning-based BnB improves maximum common subgraph search efficiency.
problem Finding maximum common subgraphs efficiently.
method Inspired by reinforcement learning, a heuristic to reach tree leaves early.
result Significantly reduces search tree size and outperforms existing BnB algorithms.
The memory capacity of linear echo state networks is accurately calculated using new numerical methods.
problem Numerical evaluations of memory capacity in recurrent neural networks often contradict theoretical bounds.
method Developed robust numerical approaches exploiting MC neutrality with respect to the input mask matrix.
result Memory curves fully agree with theory when using the proposed methods.
Most classification algorithms used in high energy physics fall under the category of supervised machine learning. Such methods require a training set containing both signal and background events and are prone to classification errors should this training data be systematically inaccurate for example due to the assumed…
Paper confirms MCS spaces are equivalent to CS sets.
problem Understanding the equivalence of MCS and CS sets.
method Analyzing the MCS stratification and intrinsic stratification.
result MCS spaces are equivalent to CS sets with respect to their stratification.
RQMC improves optimization in variational Bayes problems.
problem Optimizing variational Bayes problems with noisy objective functions.
method Use of randomized quasi-Monte Carlo (RQMC) sampling with stochastic L-BFGS.
result RQMC can significantly speed up optimization and find better parameter values.
Nonlinear RNNs' memory capacity varies widely, making it impractical.
problem The usefulness of memory capacity as a metric for linear RNNs is questioned.
method Analysis of random nonlinear RNNs with varying input scales.
result Memory capacity of nonlinear RNNs is arbitrary and impractical.
Improved barrier option pricing in Heston model using COS-BEM method.
problem Efficient barrier option pricing in the Heston model.
method Combining Fourier-cosine series (COS) method with Boundary Element Method (BEM).
result Significant computational efficiency improvement and BEM attractiveness for practitioners.
Let X X X be a non-compact geometrically finite hyperbolic 3-manifold without cusps of rank 1. The deformation space $\mc{H}$ of X X X can be identified with the Teichmüller space $\mc{T}$ of the conformal boundary of X X X as the graph of a section in $T^*\mc{T}$ . We construct a Hermitian holomorphic line bundle $\mc{L}$ on…
New algebraic structures help categorify link invariants.
problem Classifying and distinguishing links and virtual links.
method Introducing mc-biquandles and categorifying homsets.
result New link invariants defined via mc-biquandle coloring quivers.
A new method combines MLMC and particle filters for more efficient option pricing.
problem Efficiently pricing options with reduced computational effort.
method Multilevel Particle Filter (MLPF) combining MLMC and particle filters.
result MLPF demonstrates computational savings over Particle Filter (PF) for option pricing.
MC-CP combines adaptive MC dropout with conformal prediction for robust uncertainty quantification.
problem Deploying deep learning models in safety-critical applications requires reliable confidence estimates.
method MC-CP integrates adaptive Monte Carlo dropout with conformal prediction to improve model performance.
result MC-CP significantly outperforms state-of-the-art UQ methods in both classification and regression tasks.
We determine the homogeneous Kähler diffeomorphism F C FC F C which expresses the Kähler two-form on the Siegel-Jacobi ball $\mc{D}^J_n=\C^n\times \mc{D}_n$ as the sum of the Kähler two-form on $\C^n$ and the one on the Siegel ball $\mc{D}_n$ . The classical motion and quantum evolution on $\mc{D}^J_n$ determined by a hermiti…
We give a homological characterization of n n n -manifolds whose universal covering $\Wi M$ has Gromov's macroscopic dimension $\dim_{mc}\Wi M<n$ . As the result we distinguish dim m c \dim_{mc} dim m c from the macroscopic dimension dim M C \dim_{MC} dim M C defined by the author \cite{Dr}. We prove the inequality $\dim_{mc}\Wi M<\dim_{MC}\Wi M=n$ f…
New method speeds up option pricing for rough Bergomi model.
problem Time-consuming option pricing under rough Bergomi model.
method Hierarchical adaptive sparse grids and quasi Monte Carlo.
result Substantial computational gains over standard Monte Carlo.
A fast single-shot MC dropout method for neural networks.
problem Inability of DNNs to provide uncertainty measures for new situations.
method Analytically approximates MC dropout for fully connected networks.
result Approach preserves BDNN advantages while being faster.
Batch normalisation doesn't affect variational inference but fails for larger batch sizes.
problem Failure of Monte Carlo Batch Normalisation (MCBN) for capturing epistemic uncertainty in larger batch sizes.
method Investigated MCBN as an approximate inference technique for Bayesian neural networks, showing its limitations and providing insights for improvement.
result For larger batch sizes, MCBN fails to capture epistemic uncertainty, requiring the batch size to be a variational parameter.
DPMC improves inverse problem solving with MCMC, reducing error in noisy conditions.
problem Inaccurate posterior approximation in inverse problems with high noise levels.
method DPMC uses Annealed MCMC to sample through a series of intermediate distributions, reducing accumulated error.
result DPMC outperforms DPS in various inverse problems, reducing error and evaluations.
Qualitative analysis of MC dropout for NN model uncertainty.
problem Measuring uncertainty in neural network models.
method Mathematical formulation of Monte Carlo dropout and its benefits/costs in NN models.
result Potential benefits and associated costs of using MC dropout in NN models.
An efficient adaptive direct numerical integration (DNI) algorithm is developed for computing high quantiles and conditional Value at Risk (CVaR) of compound distributions using characteristic functions. A key innovation of the numerical scheme is an effective tail integration approximation that reduces the truncation …
Paper detects gradual changes in cluster structure using MC fusion.
problem Detecting gradual changes in cluster structure over time.
method MC fusion for multiple mixture numbers, examining MC transition.
result Accurately captures cluster structure during transitional periods.
We study the structure of classical groups of equivalences for smooth multigerms f : ( N , S ) → ( P , y ) f \colon (N,S) \to (P,y) f : ( N , S ) → ( P , y ) , and extend several known results for monogerm equivalences to the case of mulitgerms. In particular, we study the group $\A$ of source- and target diffeomorphism germs, and its stabilizer $\A_f$ . For monogerms $…
ADRL improves participant selection in MCS systems.
problem Designing a participant selection algorithm for different MCS systems with multiple goals.
method Auxiliary-task based deep reinforcement learning (ADRL) using transformers and pointer networks.
result ADRL outperforms other baselines in various MCS settings.
Proposes mCS for multivariate selection with FDR control.
problem Selecting high-quality candidates from multivariate datasets.
method Introduces regional monotonicity and multivariate nonconformity scores.
result Significantly improves selection power with FDR control.
Compressed Monte Carlo improves efficiency in Bayesian inference.
problem Efficiently approximating posterior distributions in Bayesian models.
method Introduces Compressed Monte Carlo (C-MC) to compress statistical information.
result C-MC schemes outperform traditional methods in particle filtering and adaptive IS algorithms.
GLSearch uses GNN to learn efficient search strategies for finding large common subgraphs.
problem Finding the Maximum Common Subgraph (MCS) between two graphs is NP-hard and hard to solve efficiently.
method GLSearch combines GNN and DQN to learn optimal node pairs for expansion in a branch and bound algorithm.
result GLSearch finds significantly larger common subgraphs than heuristic search methods given the same computation budget.
This study quantifies the scalability of k-Sliced Mutual Information (k-SMI) with dimension.
problem Understanding how SMI and its estimation rates depend on the ambient dimension.
method Developed k-SMI framework and derived bounds on MC estimates, established optimal convergence rates, and provided asymptotic results.
result Sharp bounds and optimal convergence rates for k-SMI estimation, revealing interplay with dimension and sample size.
Active Kriging Monte Carlo simulation method with conformal certification for failure probability estimation
problem Failure probability estimation in structural reliability analysis
method Active learning framework with conformal prediction
result Improved uncertainty quantification and reliability of failure probability estimates
Generative model prices basket options efficiently.
problem Real-time pricing of basket options with varying market inputs.
method Truncated path signatures and Mixture Density Networks (MDN) for learning the terminal density.
result The model produces small pricing errors and matches Monte Carlo simulations closely.
MC Dropout is re-evaluated as not Bayesian, affecting predictive posterior and multimodality.
problem MC Dropout's Bayesian properties and predictive posterior are questioned.
method Re-evaluation of MC Dropout's properties, including a new VI engine in pytorch.
result MC Dropout does not produce a faithful Bayesian predictive posterior.
MC-LSTM extends LSTM to conserve mass in neural networks.
problem Conservation laws in real-world systems.
method Extending LSTM's inductive bias to conserve mass.
result MC-LSTM sets new state-of-the-art for predicting peak flows.
The paper proves geodesic convexity and plurisubharmonicity of energy functions on Teichmüller space.
problem Geodesic convexity and plurisubharmonicity of energy functions on Teichmüller space.
method First and second variations of energy function, strict plurisubharmonicity, and convexity proofs.
result Strict plurisubharmonicity of log(E(z)) on Teichmüller space, and convexity of E(t) along Weil-Petersson geodesics.
In this analytical study we derive the optimal unbiased value estimator (MVU) and compare its statistical risk to three well known value estimators: Temporal Difference learning (TD), Monte Carlo estimation (MC) and Least-Squares Temporal Difference Learning (LSTD). We demonstrate that LSTD is equivalent to the MVU if …
A new method fills missing labels in multi-label classification problems.
problem Missing feature and label values in multi-label classification.
method Proposes co-completion (COCO) algorithm based on subgradient descent.
result Demonstrates theoretical and practical effectiveness of COCO.
For a Legendrian knot L in R^3 with a chosen Morse complex sequence (MCS) we construct a differential graded algebra (DGA) whose differential counts "chord paths" in the front projection of L. The definition of the DGA is motivated by considering Morse-theoretic data from generating families. In particular, when the MC…