arXiv research

New model for display advertising with stochastic and adversarial components.

Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests. Despite its rich applications, theoretical convergence analysis remains largely ope…

Paper explores stochastic algorithms for PCA, focusing on convergence and runtime.

Neural network based generative models with discriminative components are a powerful approach for semi-supervised learning. However, these techniques a) cannot account for model uncertainty in the estimation of the model's discriminative component and b) lack flexibility to capture complex stochastic patterns in the la…

Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from risk-adjusted discounting, we use Perron-Frobenius Theory to isolate a positive martingal…

New algorithm improves source separation with multi-trial supervision.

Paper analyzes online tensorial ICA convergence with stochastic approximation.

Deep ensembles effectively capture epistemic uncertainty through training stochasticity, providing a frequentist perspective.

New method reduces mixture model evaluation cost for large models.

Study the averaging principle for non-autonomous slow-fast systems and apply it to financial local stochastic volatility models.

It is known that the implied volatility skew of FX options demonstrates a stochastic behavior which is called stochastic skew. In this paper we create stochastic skew by assuming the spot/instantaneous variance correlation to be stochastic. Accordingly, we consider a class of SLV models with stochastic correlation wher…

This paper explores the non-convex composition optimization in the form including inner and outer finite-sum functions with a large number of component functions. This problem arises in some important applications such as nonlinear embedding and reinforcement learning. Although existing approaches such as stochastic gr…

In this paper, we provide conditions which ensure that stochastic Lipschitz BSDEs admit Malliavin differentiable solutions. We investigate the problem of existence of densities for the first components of solutions to general path-dependent stochastic Lipschitz BSDEs and obtain results for the second components in part…

Study variance-optimal hedging of forward curve derivatives under stochastic volatility.

SAMoSSA combines mSSA and AR for accurate time series analysis.

A new method interpolates between sampling and variational inference using stochastic mixtures.

We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for both arbitrary noise and stochastic noise settings. We also give matching minimax …

Study shows conditions for local martingales in SDEs with stochastic volatility.

We consider in this paper a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. We present a new class of first-order methods, namely the gradient sliding algorithms, which can skip the…

We solve complex SDEs to model financial volatility.

Proves existence and uniqueness of calibrated LSV model.

A new method clusters data from multiple sources using a mixture of multilayer SBMs.

New algorithm improves convergence rates for convex optimization problems.

Dynamical systems are widely used in science and engineering to model systems consisting of several interacting components. Often, they can be given a causal interpretation in the sense that they not only model the evolution of the states of the system's components over time, but also describe how their evolution is af…

In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward--backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the differentiability of a FB…

The paper develops algorithms for computing in stochastic acceptors.

Decentralized learning reduces regret by sharing model updates, especially with stochastic components.

NSGLD improves SGLD for non-convex optimization problems.

Proposes flexible auto-encoders for varying data dimensions.

Explains gradient descent methods and their convergence, focusing on simple analysis.

New methods reduce constraint violations to certainty in stochastic optimization.

This technical report proves components consistency for the Doubly Stochastic Dirichlet Process with exponential convergence of posterior probability. We also present the fundamental properties for DSDP as well as inference algorithms. Simulation toy experiment and real-world experiment results for single and multi-clu…

As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine learning and predictive modeling, distributed optimization methods have recently garne…

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…

We investigate how simultaneously recorded long-range power-law correlated multi-variate signals cross-correlate. To this end we introduce a two-component ARFIMA stochastic process and a two-component FIARCH process to generate coupled fractal signals with long-range power-law correlations which are at the same time lo…

Study uses VIX for zero-coupon Treasury rates, proving long-term stability and returns.

A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processe…

Method learns dynamics of slow variables from stochastic data.

Paper develops a new algorithm for sparse signal recovery.

Enhances mixture models with classifier-defined weights.

A new method reduces data movement in neural network training.

In Figueroa-López et al. (2013), a second order approximation for at-the-money (ATM) option prices is derived for a large class of exponential Lévy models, with or without a Brownian component. The purpose of this article is twofold. First, we relax the regularity conditions imposed in Figueroa-López et al. (2013) on t…

Study on Kyle-Back model with risk aversion and non-Gaussian beliefs.

The paper identifies key macroeconomic events affecting exchange rate volatility.

Develops robust methods for infinite-dimensional stochastic processes.

New method for asynchronous stochastic approximation converges in reinforcement learning.

Improved noise estimation in latent neural SDEs enhances model accuracy.

New method for separating mixed signals with nonlinear functions.