Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carl…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
Trend · papers per month
48 results for “low-discrepancy sequences”
In [Mas82] and [Vee78] it was proved independently that almost every interval exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem implies that these maps mainly have uniformly distributed orbits. This raises the question under which conditions the orbits yield low-discrepancy sequences. The case o…
New deep learning method outperforms random training data.
problem Improving accuracy of deep learning algorithms in high dimensions.
method Training with low-discrepancy sequences instead of random data.
result Significantly outperforms standard deep learning algorithms.
Langevin Quasi-Monte Carlostat.CO
LMC improves sampling from complex distributions using quasi-random sequences.
problem Sampling from complex high-dimensional distributions with high accuracy.
method Using completely uniformly distributed (CUD) sequences in Langevin Monte Carlo (LMC) to generate Gaussian perturbations.
result LMC with low-discrepancy CUD sequences achieves smaller estimation error than standard LMC.
Comparative Study of Monte Carlo and Quasi-Monte Carlo Techniques for Enhanced Derivative Pricingq-fin.PR
This study compares MC and QMC methods for derivative pricing, showing QMC's superior convergence rates.
problem Improving derivative pricing accuracy and efficiency in high-dimensional settings.
method Compared Monte Carlo and quasi-Monte Carlo techniques, focusing on convergence rates and low-discrepancy sequences.
result Quasi-Monte Carlo methods achieve superior convergence rates and reduce root mean square error in derivative pricing.
This paper defines the notion of class discrepancy for families of functions. It shows that low discrepancy classes admit small offline and streaming coresets. We provide general techniques for bounding the class discrepancy of machine learning problems. As corollaries of the general technique we bound the discrepancy …
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are mostly not scalable. In this paper, we develop a method that transforms the quadra…
MPMC generates low-discrepancy points using graph neural networks.
problem Generating efficient low-discrepancy point sets.
method Leveraging Graph Neural Networks to model geometric properties.
result Achieves state-of-the-art performance in generating low-discrepancy points.
Using Low-Discrepancy Points for Data Compression in Machine Learning: An Experimental Comparisonstat.ML
Two methods using low-discrepancy points improve data compression for neural networks.
problem Efficiently compress large datasets for neural network training.
method Two methods based on low-discrepancy points: digital nets with averaging and clustering.
result Second method outperforms supercompress in compression error and neural network accuracy.
We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel).…
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.
Driven by the need for parallelizable hyperparameter optimization methods, this paper studies \emph{open loop} search methods: sequences that are predetermined and can be generated before a single configuration is evaluated. Examples include grid search, uniform random search, low discrepancy sequences, and other sampl…
Statistical machine learning models should be evaluated and validated before putting to work. Conventional k-fold Monte Carlo Cross-Validation (MCCV) procedure uses a pseudo-random sequence to partition instances into k subsets, which usually causes subsampling bias, inflates generalization errors and jeopardizes the r…
Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysisq-fin.RM
We review and apply Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques to pricing and risk management (greeks) of representative financial instruments of increasing complexity. We compare QMC vs standard Monte Carlo (MC) results in great detail, using high-dimensional Sobol' low discrepancy sequen…
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.
This thesis advances algorithms and software for QMC, GP, and sciML.
problem Efficient high-dimensional integration, interpolation, and PDE modeling.
method Developed new algorithms and software for QMC, GP, and sciML.
result Efficient and accurate methods for high-dimensional problems.
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where the function oscillates more, while allocating the samples such that they are wel…
Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeksq-fin.CP
QMC and GSA improve option pricing and risk measures efficiency.
problem Efficiently pricing and hedging complex financial instruments.
method Application of QMC and GSA techniques for financial instrument pricing and hedging, comparing MC vs QMC and analyzing greeks computation.
result QMC outperforms MC in most cases, especially in high-dimensional simulations, leading to faster and more stable convergence.
Improved algorithm for low-discrepancy colorings with practical time complexity.
problem Finding near-optimal colorings for set systems with low discrepancy.
method Randomized algorithm using primal-dual reweighing and matchings with low crossing number.
result Improved time complexity for constructing colorings and approximations.
Optimizes kernel discrepancies by selecting subsets efficiently.
problem Improving kernel discrepancies for QMC methods.
method Introduces a novel subset selection algorithm for kernel discrepancies.
result Efficiently generates low-discrepancy samples from various distributions.
Samplets and multiwavelets constructed from scattered data converge to specific densities in the limit.
problem Constructing data-adapted multiresolution analyses and multiwavelets with flexible vanishing moments.
method Probabilistic framework for samplet construction; convergence to multiwavelets with broken polynomial densities.
result Samplet construction converges to multiwavelets in the infinite data limit.
Transport Quasi-Monte Carlomath.NA
Improves QMC for complex distributions using transport maps.
problem Challenges in applying QMC to general target distributions.
method Train a transport map to approximate target distributions, ensuring RQMC achieves superior error rates.
result Transport QMC achieves faster convergence rates than standard Monte Carlo under mild conditions.
Although the sequence-to-sequence (encoder-decoder) model is considered the state-of-the-art in deep learning sequence models, there is little research into using this model for recovering missing sensor data. The key challenge is that the missing sensor data problem typically comprises three sequences (a sequence of o…
Classifies intrinsically linked tournaments by their score sequences.
problem Classifying intrinsically linked tournaments using their score sequences.
method Examining the score sequences of tournaments and identifying linkless sequences.
result The vast majority of score sequences for 8-vertex tournaments are linkless.
Enhances sequence memory capacity in neural networks.
problem Limited sequence capacity in Hopfield-like neural networks.
method Introducing a nonlinear interaction term and a generalized pseudoinverse rule.
result Significantly increased sequence capacity with novel scaling laws.
Deep generative models have been successfully used to learn representations for high-dimensional discrete spaces by representing discrete objects as sequences and employing powerful sequence-based deep models. Unfortunately, these sequence-based models often produce invalid sequences: sequences which do not represent a…
Equivalent condition found for q-holonomic sequences.
problem Characterizing q-holonomic sequences.
method Elimination property for subsets of variables.
result Proved equivalence of q-holonomicity and elimination property.
The abstract discusses a spectral sequence for Lie algebroids.
problem The abstract tackles the spectral sequence of Lie algebroids.
method The abstract presents a spectral sequence for Lie algebroids, generalizing classical constructions.
result The spectral sequence converges to Lie algebroid cohomology for wide Lie subalgebroids and to formal Lie algebroid cohomology for Lie subalgebroids over proper submanifolds.
Many machine learning tasks can be expressed as the transformation---or \emph{transduction}---of input sequences into output sequences: speech recognition, machine translation, protein secondary structure prediction and text-to-speech to name but a few. One of the key challenges in sequence transduction is learning to …
Mining tasks over sequential data, such as clickstreams and gene sequences, require a careful design of embeddings usable by learning algorithms. Recent research in feature learning has been extended to sequential data, where each instance consists of a sequence of heterogeneous items with a variable length. However, m…
Paper proposes using LSTM for LSH-based sequence alignment.
problem Sequence alignment using deep learning models.
method Deep bidirectional LSTM for feature learning and LSH-based sequence alignment.
result Higher accuracy achieved with LSTM-based model.
Study on continuous sequence classification with distribution uncertainty.
problem Classifying continuous sequences with varying distribution uncertainty.
method Proposes distribution-free tests for three test designs: fixed-length, sequential, and two-phase tests.
result Error probabilities decay exponentially fast for all test designs.
Deep learning models optimize protein sequences.
problem Optimizing protein properties through sequence design.
method Deep generative models guided by machine learning.
result Improved protein sequence generation from prior knowledge.
Sequence classification is an important data mining task in many real world applications. Over the past few decades, many sequence classification methods have been proposed from different aspects. In particular, the pattern-based method is one of the most important and widely studied sequence classification methods in …
We study the Thompson sampling algorithm in an adversarial setting, specifically, for adversarial bit prediction. We characterize the bit sequences with the smallest and largest expected regret. Among sequences of length with zeros, the sequences of largest regret consist of alternating zeros and …
Unimodal sequences of moves connect 3-manifold triangulations.
problem Understanding the structure of sequences of bistellar flips.
method Examined unimodal sequences of moves that increase and decrease triangulation size.
result Proved that any two one-vertex triangulations are connected by a unimodal sequence of moves.
This paper presents a novel end-to-end approach to program repair based on sequence-to-sequence learning. We devise, implement, and evaluate a system, called SequenceR, for fixing bugs based on sequence-to-sequence learning on source code. This approach uses the copy mechanism to overcome the unlimited vocabulary probl…
This work compresses sequences by treating them as continuous-time processes, enabling efficient discretization.
problem Efficient compression of sequences, especially with deep learning models that scale with sequence length.
method Treat sequences as continuous-time processes, learn efficient discretization, and decode at different time intervals.
result Automatic bit rate reductions in video and motion capture sequences using learned discretization.
Characterizes sequences from two-component link diagrams.
problem Understanding information from non-self crossing sequences of link diagrams.
method Investigated and characterized pairs of non-self OU sequences of two-component link diagrams.
result Completely characterized pairs of non-self OU sequences of diagrams of two-component links.
In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we introduce the inconstancy of a sequence and we show why it seems more pertinent …
Generative adversarial nets (GAN) has been successfully introduced for generating text to alleviate the exposure bias. However, discriminators in these models only evaluate the entire sequence, which causes feedback sparsity and mode collapse. To tackle these problems, we propose a novel mechanism. It first segments th…
Researchers develop flexible kernels for biological sequences with guaranteed reliability.
problem Challenges in applying machine learning to biological sequences, including unreliable methods.
method Theoretical analysis and development of modified kernels to ensure reliability and accuracy.
result Developed kernels that are universal, characteristic, and metrize the space of distributions for biological sequences.
A convolutional sequence to sequence non-intrusive load monitoring model is proposed in this paper. Gated linear unit convolutional layers are used to extract information from the sequences of aggregate electricity consumption. Residual blocks are also introduced to refine the output of the neural network. The partiall…
Using sequence to sequence algorithms for query expansion has not been explored yet in Information Retrieval literature nor in Question-Answering's. We tried to fill this gap in the literature with a custom Query Expansion engine trained and tested on open datasets. Starting from open datasets, we built a Query Expansi…
P3BO optimizes biological sequence design by combining multiple methods.
problem Variability in performance of black-box optimization methods for biological sequence design.
method Population-Based Black-Box Optimization (P3BO) that samples sequences from an ensemble of methods, weighting by past performance.
result P3BO outperforms individual methods, proposing higher quality and more diverse sequences.
Undirected neural sequence models such as BERT (Devlin et al., 2019) have received renewed interest due to their success on discriminative natural language understanding tasks such as question-answering and natural language inference. The problem of generating sequences directly from these models has received relativel…
New concordance invariant from spectral sequence on Khovanov homology.
problem Concordance invariants from spectral sequences.
method Constructing from spectral sequence on Khovanov homology.
result Provides a bound on the nonorientable slice genus.
The availability of large amounts of time series data, paired with the performance of deep-learning algorithms on a broad class of problems, has recently led to significant interest in the use of sequence-to-sequence models for time series forecasting. We provide the first theoretical analysis of this time series forec…