Adaptive DBSCAN improves clustering for varying density clusters.
problem Reduced performance for clusters with different densities.
method Proposes an adaptive DBSCAN algorithm.
result Significantly improves performance for varying density clusters.
Estimates financial market impacts of COVID-19 using time-varying kernel density.
problem Estimating the impact of COVID-19 on financial markets over time.
method Time-varying kernel density estimation with Kolmogorov-Smirnov statistic.
result Determines the chronology and regional disparities of financial market impacts.
Improved Mapper algorithm for datasets with varying density.
problem Difficulty in tuning resolution for datasets with varying density.
method Generalized cover type and incorporated lens-space density into the cover.
result Graph produced by Mapper converges to Reeb graph of Rips complex.
Study shows volume density in central harmonic spaces can vary arbitrarily.
problem Volume density in central harmonic spaces can vary arbitrarily.
method Analyzes asymptotics of volume density function in central harmonic manifolds.
result Volume density in central harmonic spaces can be specified arbitrarily and does not determine geometry.
DADC algorithm improves clustering for data with varying density.
problem Sparse cluster loss and cluster fragmentation in density peak clustering.
method Domain-adaptive density measurement, cluster center self-identification, and cluster self-ensemble.
result DADC achieves more reasonable clustering results on data with varying density.
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.
CRAD clusters data with robust depth-based dissimilarity, outperforming existing methods.
problem Clustering data with varying densities and unknown true number of clusters.
method CRAD uses a robust data depth as dissimilarity measure and a novel neighbor searching function.
result CRAD outperforms DBSCAN, OPTICS, and DBCA in detecting clusters with varying densities.
BDMBC clusters data with varying densities using a new PLLS measure.
problem Finding clusters with varying densities in data.
method Bagged k-distance with PLLS for mode estimation. result BDMBC achieves optimal convergence rates for mode and level set estimation.
In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in R3. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By var…
The study shows how geometric Weyl bulk-density exponent rigidifies spectral encodings in O-regularly varying classes.
problem Understanding spectral encodings under Weyl growth conditions.
method Analyzing geometric Weyl bulk-density exponent and proving spectral rigidity.
result The geometric Weyl bulk-density exponent (d−2)/2 rigidifies spectral encodings in the O-regularly varying class, leading to unique admissible exponents and scaling laws. A new method combines spectral and density-based clustering for robust nonconvex clustering.
problem Finding robust clusterings for nonconvex shapes with varying densities and noise.
method Combining spectral and density-based clustering approaches to optimize a density criterion.
result Our method provides robust and reliable clusterings on synthetic and real-world data.
Develops diffusion models for time-varying correlation on the circle.
problem Time-varying correlation modeling on the circle.
method Stochastic processes on the unit circle, specifically Brownian motion and von Mises diffusion.
result Derives an accurate analytical approximation to the transition density of the von Mises diffusion.
FNFs model parameter-dependent densities by combining a fixed flow with a polynomial parameter-dependent transformation.
problem Learning a separate flow for every parameter configuration is intractable.
method Factorizable Normalizing Flows (FNFs) represent the parameter-dependent density as a fixed flow for a reference configuration and a learnable polynomial transformation factorized over parameters.
result FNFs enable the recovery of the combined effect of multiple parameters without sampling their joint space, providing a scalable and interpretable solution.
This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over time using a modified form of the Gram-Charlier density in which skewness and ku…
LAAT detects multiple low-density manifolds in noisy data.
problem Detecting multiple low-density manifolds in noisy data.
method Locally Aligned Ant Technique (LAAT) based on Ant Colony Optimization.
result LAAT recovers multiple manifolds in extremely noisy data.
Proposes a new hierarchical clustering method combining DP and DBSCAN strengths.
problem Combining strengths of DP and DBSCAN for arbitrary shape clusters.
method DC-HDP: Combines Density Peak and Density-Connectivity approaches.
result Produces best clustering results on 14 datasets.
Bayesian DDR models complex multivariate distributions.
problem Modeling relationships between multivariate distributions with differing dimensions.
method Generalized Bayesian framework using sliced Wasserstein distance and MALA for inference.
result Posterior consistency and robust fits demonstrated in simulations and real data.
A new tensor ring mixture model improves density estimation efficiency.
problem Efficient probability density estimation in statistical machine learning.
method Tensor ring decomposition with mixture model for adaptive weights.
result Enhanced expressive capability and flexibility in density estimation.
Develops diffusion samplers for target distributions with efficient score and density estimates.
problem Estimating scores and densities for time-varying distributions.
method Sequential Monte Carlo with diffusion paths and control variates.
result Effective samplers for time-varying distributions with theoretical guarantees and practical applications.
Derives continuum model from discrete ε-graphs with connectivity functional.
problem Modeling diffusion in networks with varying connectivity.
method Energy-based continuum limit derivation, neural-network reconstruction of connectivity.
result Error between discrete and continuum energies is O(ε), valid even with fluctuations. A new type of diffeomorphic normalizing flow for flexible density estimation.
problem Flexible density estimation and variational inference.
method Constructs a diffeomorphic flow using an ODE with a neural network to parametrize the smooth vector field and a recursive neural network for approximating the solution.
result End-to-end trained DDNF achieves competitive results on density estimation and variational inference tasks.
A new method generates counterfactual treatment outcomes for time-varying treatments.
problem Estimating counterfactual outcomes for time-varying treatments with high-dimensional outcomes.
method Conditional generative framework with inverse probability re-weighting.
result Our method outperforms state-of-the-art baselines in generating high-quality counterfactual samples.
Variational inference provides a powerful tool for approximate probabilistic in- ference on complex, structured models. Typical variational inference methods, however, require to use inference networks with computationally tractable proba- bility density functions. This largely limits the design and implementation of v…
This paper tackles continuous covariate shift by adaptively training predictors.
problem Continuous covariate shift where input distributions change over time.
method Online density ratio estimation method to adaptively train predictors.
result Excess risk guarantee for the predictor through dynamic regret bound.
Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such models can be very computationally expensive when there are many datapoints and …
New CTRL algorithm adapts to varying problem difficulty.
problem Adapting to varying levels of problem difficulty in CTRL.
method MLE with a general function approximator, estimating state marginal density.
result Regret bound scales with reward variance and measurement resolution, independent of measurement strategy.
BASS efficiently learns time-varying graphs with low complexity and automatic tuning.
problem Estimating time-varying graphical models with efficient and automatic parameter tuning.
method BASS uses temporally-dependent spike-and-slab priors and variational inference to learn graph structures efficiently.
result BASS outperforms existing methods in recovering true graphs, especially for high-dimensional cases.
Enhances FAVAR models with autoencoder for better economic forecasting and interpretability.
problem Limitations of linear FAVAR models in forecasting and structural analysis.
method Introduces Grouped Sparse autoencoder with time-varying parameters.
result The Grouped Sparse autoencoder produces more interpretable factors and superior forecasting performance.
Bayesian models improve cryptocurrency forecasting accuracy.
problem Improving cryptocurrency forecasting accuracy using Bayesian models.
method Compared Bayesian models with constant and time-varying volatility, including stochastic volatility and GARCH models.
result Stochastic volatility significantly outperforms VAR in both point and density forecasting.
Accurate and reliable predictions of infectious disease dynamics can be valuable to public health organizations that plan interventions to decrease or prevent disease transmission. A great variety of models have been developed for this task, using different model structures, covariates, and targets for prediction. Expe…
A new kernel Stein test assesses fit for variable-length sequential data.
problem Evaluating goodness of fit for varying-dimensional data like text documents of different lengths.
method Extends kernel Stein discrepancy (KSD) to variable-dimension settings by identifying appropriate Stein operators and proposing a novel KSD goodness-of-fit test.
result The proposed test performs well on discrete sequential data benchmarks.
New sampling method uses gradient-free IPS with RKHS velocity field.
problem Efficient sampling from unnormalized target densities.
method Gradient-free interacting particle systems (IPS) with RKHS velocity field.
result IPS produce high-quality samples from various target distributions.
Robustly infers manifold density and geometry under high-dimensional noise.
problem Inaccurate kernel density estimation under high-dimensional noise.
method Doubly stochastic normalization of Gaussian kernel.
result Robust tools for density estimation, noise magnitude estimation, and distance approximation.
Adaptive ML learns complex time-varying systems without new data.
problem Applying ML to time-varying systems with shifting distributions.
method Mapping high-dimensional inputs to low-dimensional latent space, actively tuning latent space based on feedback.
result Learning correlations and tracking system evolution in real-time without new data.
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of…
Study on continuity of solutions for complex Monge-Ampère equations with movable singularities.
problem Continuity of solutions with prescribed singularities for complex Monge-Ampère equations.
method Strong continuity methods with movable singularities, including Kähler-Einstein metrics.
result Sufficient conditions for strong continuity of solutions and openness results for Fano type equations.
A new MCMC method combines low and high-fidelity models to reduce computation.
problem Inefficient computation of expensive target densities in scientific applications.
method Pseudo-marginal MCMC approach using a telescoping series of low-fidelity models.
result Asymptotically exact multi-fidelity MCMC algorithms for reduced computational cost.
Lumbermark clusters data robustly, slicing limbs of mutual reachability trees.
problem Detecting clusters of varying sizes, densities, and shapes in datasets.
method Iteratively chops limbs of a mutual reachability minimum spanning tree.
result Lumbermark produces partitions with user-specified sizes.
We develop a novel "decouple-recouple" dynamic predictive strategy and contribute to the literature on forecasting and economic decision making in a data-rich environment. Under this framework, clusters of predictors generate different latent states in the form of predictive densities that are later synthesized within …
A new method detects anomalies in trajectory data using normalizing flows.
problem Detecting anomalous patterns in high-dimensional, varying-length spatial data.
method Probability density estimation via normalizing flows for each trajectory segment, aggregating likelihoods.
result The proposed method, GRADINGS, effectively identifies anomalies in real-world trajectory data.
Let X⊂Rn be a connected locally closed definable set in an o-minimal structure. We prove that the following three statements are equivalent: (i) X is a C1 manifold, (ii) the tangent cone and the paratangent cone of X coincide at every point in X, (iii) for every x∈X, the tangent cone of…
UAPCA projects uncertain data to low dimensions using GMMs.
problem Uncertain multidimensional data not well described by normal distributions.
method Model data with Gaussian mixture models, derive UAPCA projection from general formulation.
result Low-dimensional projections better represent multidimensional distributions.
The paper analyzes Kernel Density Estimation in high dimensions with varying data and dimensionality.
problem High-dimensional Kernel Density Estimation with growing data and dimensionality.
method Examines the behavior of Kernel Density Estimators in the regime where both data points and dimensionality grow with a fixed ratio.
result Three distinct statistical regimes are identified for Kernel-based density estimates, each with different statistical properties.
Improved RBF-FD method for financial derivatives pricing.
problem Efficient pricing of financial derivatives with robust methods.
method Polyharmonic splines and smoothly varying node layouts for RBF-FD methods.
result Significantly improved performance in pricing financial derivatives.
In a recent work (Chattopadhyay, A. K. et al, Europhys. Lett. {\bf 91}, 58003, 2010) based on food consumption statistics, we showed how a stochastic agent based model could represent the time variation of the income distribution statistics in a developing economy, thereby defining an alternative \enquote{poverty index…
This paper compares log-likelihood and BLEU scores for sequence generation tasks.
problem The discrepancy between density estimation and sequence generation performance.
method Comparing several density estimators on five machine translation tasks.
result The correlation between log-likelihood and BLEU varies depending on model families.
Algorithm learns graph ARMA processes for missing signal estimation.
problem Missing signal estimation in time-varying graph signals.
method Learning joint time-vertex power spectral density through convex relaxations.
result High accuracy in time-vertex signal estimation.
In this paper a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with empirical findings from option price data. The model is constructed with the aim of bei…