Paper extends stochastic dominance for compound binomial distributions.
problem Stochastic dominance for infinite-mean random variables.
method Investigates properties and inclusion relationships of distribution classes, extends results to compound binomial distributions.
result Establishes necessary and sufficient conditions for first-order stochastic dominance preservation.
New class of heavy-tailed distributions shows weighted averages dominate individual variables.
problem Understanding and comparing risks in heavy-tailed distributions.
method Introducing a new class of heavy-tailed distributions and proving stochastic dominance relations.
result Weighted averages of random variables in this class are stochastically larger than individual variables.
In this article, we advocate the ensemble approach for variable selection. We point out that the stochastic mechanism used to generate the variable-selection ensemble (VSE) must be picked with care. We construct a VSE using a stochastic stepwise algorithm, and compare its performance with numerous state-of-the-art algo…
Method learns dynamics of slow variables from stochastic data.
problem Modeling unknown multiscale stochastic systems with limited data.
method Data-driven approach to learn effective dynamics from bursts of observation data.
result Generative model accurately captures effective dynamics of slow variables.
How to model distribution of sequential data, including but not limited to speech and human motions, is an important ongoing research problem. It has been demonstrated that model capacity can be significantly enhanced by introducing stochastic latent variables in the hidden states of recurrent neural networks. Simultan…
DSVNP uses global and local latent variables for improved neural process predictions.
problem Limited expressiveness of vanilla neural processes in capturing target-specific local variation.
method Introduces DSVNP combining global and local latent variables for prediction.
result Competitive prediction performance in multi-output regression and uncertainty estimation.
Unexpectedly, weighted Pareto variables are stochastically dominant.
problem Understanding stochastic dominance in Pareto distributions.
method Analyzing weighted averages of Pareto random variables with infinite mean.
result The weighted average of Pareto variables is stochastically dominant.
Simplified calculus for semimartingales makes complex transformations easier.
problem Complex transformations of semimartingales.
method Unified treatment of transformations for real and complex semimartingales.
result Unified calculus for semimartingales simplifies various transformations.
The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propag…
Paper presents deep LSMC method for efficient variable annuity pricing.
problem Efficiently pricing variable annuities with guarantees using simulation methods.
method Modifies least-squares Monte Carlo (LSMC) algorithm for optimal stochastic control problems.
result Deep LSMC provides more stable and robust pricing performance for higher-dimensional problems.
Diversification improves profits for heavy-tailed investments.
problem Investment portfolios of Pareto-distributed returns.
method Stochastic dominance and majorization order.
result Diversification increases first-order stochastic dominance for heavy-tailed returns.
Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic process, and MCMC moves to propose new values for the parameters. We show how p…
A new graphical method compares stochastic variables visually.
problem Comparing non-deterministic measurements visually.
method Cumulative distribution function dominance measure and quantile decomposition.
result Additional conclusions missed by other methods can be inferred.
We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financia…
Enhances deep kernel learning with stochastic latent variables for better model regularization.
problem Weak model regularization in deep kernel learning, especially on small datasets.
method Introduces DLVKL model with stochastic latent variables, NSDE for expressive posterior, and hybrid prior.
result DLVKL-NSDE outperforms existing deep GPs on large datasets.
Deep learning improves stochastic downscaling of climate variables.
problem Accurately capturing climatic variability at local scales.
method Proposed improvements to GANs for stochastic downscaling of climate variables.
result Improved stochastic calibration of GANs for high-resolution climate predictions.
Paper establishes sufficient condition for comparing linear combinations of infinite-mean risks.
problem Comparing linear combinations of infinite-mean risks under stochastic dominance.
method Introduced a new class of distributions and used majorization order to compare weights.
result Linear combinations of random variables are stochastically larger when their weight vectors are smaller in majorization order.
The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us to derive a metric of maximum mean discrepancy type for laws of stochastic proce…
Enhances valuation of variable annuities with stochastic interest rate models.
problem Valuation and optimal surrender strategies for variable annuities in Lévy models.
method Hybrid numerical method combining tree methods for interest rate modeling and finite difference techniques for asset price.
result Influence of stochastic interest rates on surrender decisions and contract design.
A new method for efficient inference in probabilistic programs with mixed support.
problem Challenges in inference for programs with both continuous and discrete latent variables.
method Stochastic gradient Markov Chain Monte Carlo algorithms.
result Outperforms existing composing inference baselines and works almost as well as inference in marginalized versions.
We study the performance of stochastically trained deep neural networks (DNNs) whose synaptic weights are implemented using emerging memristive devices that exhibit limited dynamic range, resolution, and variability in their programming characteristics. We show that a key device parameter to optimize the learning effic…
Paper introduces multitask neural networks for efficient stochastic control problems.
problem Infeasibility of simulating state variables in some stochastic control problems.
method Multitask neural networks with dynamic task balancing.
result Multitask neural networks outperform state-of-the-art approaches in derivatives pricing problems.
A scalable GPLVM model using stochastic variational inference.
problem Scalable inference for Gaussian process latent variable models.
method Doubly stochastic formulation of Bayesian GPLVM with minibatch training.
result High-fidelity reconstructions in the presence of missing data.
Stochastic neural networks with infinite width become deterministic, reducing training variance.
problem Understanding how stochasticity in neural networks affects learning and regularization.
method Theoretical analysis of stochastic neural networks with infinite width.
result As the width of an optimized stochastic neural network increases, its predictive variance on the training set decreases to zero.
New algorithms for IV regression with streaming data, avoiding matrix inversions.
problem Instrumental variable regression with streaming data.
method Viewing IV regression as a stochastic optimization problem, developing algorithms that avoid matrix inversions and mini-batches.
result Rates of convergence of order O(logT/T) and O(1/T1−ι) for linear models. New algorithm tackles big data Bayesian problems with latent variables.
problem Bayesian computing for large-scale problems with missing data and dimension jumping.
method Extended stochastic gradient MCMC with latent variables.
result Highly scalable and more efficient than traditional MCMC algorithms.
SGD improves generalization by using gradient variability as a proxy for data randomness.
problem Improving generalization in machine learning models trained with stochastic gradient descent.
method Bootstrap perspective on SGD, analyzing gradient variability and algorithmic variability.
result SGD avoids spurious solutions and improves generalization by implicitly regularizing the trace of the gradient covariance matrix.
Method learns model for unknown stochastic system from data.
problem Modeling unknown stochastic dynamical systems.
method Autoencoder approach using deep neural networks (DNNs).
result Decoder serves as a predictive model for unknown stochastic systems.
We introduce and compare new variability measures based on risk quantiles.
problem Comparing variability measures in risk management.
method Developed a framework for one-parameter families of inter-Expected Shortfall differences and inter-expectile differences.
result Characterized symmetric and comonotonic variability measures as mixtures of inter-Expected Shortfall differences.
It is challenging for stochastic optimizations to handle large-scale sensitive data safely. Recently, Duchi et al. proposed private sampling strategy to solve privacy leakage in stochastic optimizations. However, this strategy leads to robustness degeneration, since this strategy is equal to the noise injection on each…
We develop a new statistical test for comparing variables with varying scales.
problem Comparing variables with different scales in multidimensional spaces.
method Order based on expectations of random variables, generalized stochastic dominance (GSD) order, regularized statistical test, linear optimization, imprecise probability models.
result Validated through multidimensional data from various fields.
Proposes flexible auto-encoders for varying data dimensions.
problem Fixed latent dimensions limit data flexibility.
method Stochastic bottleneck with weighted dropouts.
result Seamless variable dimensionality reduction with high performance.
Previous studies on stochastic primal-dual algorithms for solving min-max problems with faster convergence heavily rely on the bilinear structure of the problem, which restricts their applicability to a narrowed range of problems. The main contribution of this paper is the design and analysis of new stochastic primal-d…
Proposes a virtual bidding strategy for electricity markets using stochastic control.
problem Optimizing electricity prices in day-ahead and real-time markets.
method Modeling price differences as Brownian motion with meteorological variables, transforming into portfolio management problem.
result Developed a strategy to manage electricity prices efficiently.
New method tackles endogeneity in online learning with improved regret bounds.
problem Endogeneity in real data due to omitted variables, strategic behaviors, etc.
method O2SLS (Online Two-Stage Least Squares) for Instrumental Variable (IV) regression.
result O2SLS achieves identification and oracle regret bounds for stochastic online learning.
New method uses joint stochastic approximation to improve learning of discrete latent models.
problem Challenges in learning discrete latent variable models, especially with inference model gradients and log-likelihood optimization.
method Proposes a new method based on stochastic approximation theory that directly maximizes the target log-likelihood and minimizes the posterior-inference model divergence.
result Consistently outperforms recent competitive algorithms in generative modeling and structured prediction tasks.
Enhanced Black-Scholes model for option pricing with stochastic volatility and interest rate variability.
problem Improving option pricing accuracy in volatile financial markets.
method Extended Black-Scholes model using finite difference method and LSTM machine learning.
result Finite difference method outperforms LSTM in computational efficiency but not in accuracy.
I introduce a general, Bayesian method for modelling univariate time series data assumed to be drawn from a continuous, stochastic process. The method accommodates arbitrary temporal sampling, and takes into account measurement uncertainties for arbitrary error models (not just Gaussian) on both the time and signal var…
A new model encodes distances and topology in latent variables.
problem Modeling dissimilarity data with latent variables and invariances.
method Isometric Gaussian Process Latent Variable Model using Riemannian geometry and variational inference.
result The model can encode invariances in learned manifolds.
With latent variables, stochastic recurrent models have achieved state-of-the-art performance in modeling sound-wave sequence. However, opposite results are also observed in other domains, where standard recurrent networks often outperform stochastic models. To better understand this discrepancy, we re-examine the role…
New method measures model variability from stochastic optimization.
problem Measuring model quality obscured by stochastic optimization.
method Robust hypothesis testing and novel summary statistic.
result Shows α-trimming level is more expressive than performance metrics. A scalable MOGP model with stochastic variational inference for many outputs.
problem Efficiently modeling data from multiple sources with many outputs.
method Stochastic variational inference for Latent Variable MOGP (LV-MOGP).
result Computational complexity per iteration is independent of the number of outputs.
Stochastic gradient Langevin dynamics (SGLD) is a computationally efficient sampler for Bayesian posterior inference given a large scale dataset. Although SGLD is designed for unbounded random variables, many practical models incorporate variables with boundaries such as non-negative ones or those in a finite interval.…
Study market-to-book ratios using Stochastic Portfolio Theory.
problem Identify the value factor in stock returns.
method Develop functionally generated portfolios using book values and analyze their relative returns.
result The value factor (market-to-book ratio) affects portfolio performance.
Many efforts have been devoted to training generative latent variable models with autoregressive decoders, such as recurrent neural networks (RNN). Stochastic recurrent models have been successful in capturing the variability observed in natural sequential data such as speech. We unify successful ideas from recently pr…
We extend probabilistic programming to handle conditioning on marginal distributions.
problem Conditioning probabilistic programs on marginal distributions of observable variables.
method We define and implement stochastic conditioning, allowing inference in probabilistic programs conditioned on marginal distributions.
result We demonstrate the effectiveness of stochastic conditioning in various real-life scenarios.
We introduce local expectation gradients which is a general purpose stochastic variational inference algorithm for constructing stochastic gradients through sampling from the variational distribution. This algorithm divides the problem of estimating the stochastic gradients over multiple variational parameters into sma…
Convolutional architectures have recently been shown to be competitive on many sequence modelling tasks when compared to the de-facto standard of recurrent neural networks (RNNs), while providing computational and modeling advantages due to inherent parallelism. However, currently there remains a performance gap to mor…