arXiv research

We analyze how uncertainty in models affects optimization outcomes using Wasserstein distances.

Researchers quantify risk exposure and sensitivities in financial markets under model uncertainty.

Study examines how slight model changes affect multi-period optimization outcomes.

Risk management in financial derivative markets requires inevitably the calculation of the different price sensitivities. The literature contains an abundant amount of research works that have studied the computation of these important values. Most of these works consider the well-known Black and Scholes model where th…

New Monte Carlo method outperforms existing strategy for estimating Sobol' indices.

Cost-Sensitive Online Classification has drawn extensive attention in recent years, where the main approach is to directly online optimize two well-known cost-sensitive metrics: (i) weighted sum of sensitivity and specificity; (ii) weighted misclassification cost. However, previous existing methods only considered firs…

The paper calculates option prices using Mellin transform for stochastic volatility models.

CEFOL uses deep learning for dynamic programming with recursive utility.

We study the sensitivity of the expected utility maximization problem in a continuous semi-martingale market with respect to small changes in the market price of risk. Assuming that the preferences of a rational economic agent are modeled with a general utility function, we obtain a second-order expansion of the value …

Investigates model risk and semi-static hedging for martingale constrained models.

Optimizer memory affects learning rate sensitivity in shuffle order, impacting fine-tuning noise.

Online Active Learning (OAL) aims to manage unlabeled datastream by selectively querying the label of data. OAL is applicable to many real-world problems, such as anomaly detection in health-care and finance. In these problems, there are two key challenges: the query budget is often limited; the ratio between classes i…

It has been shown that dimension reduction methods such as PCA may be inherently prone to unfairness and treat data from different sensitive groups such as race, color, sex, etc., unfairly. In pursuit of fairness-enhancing dimensionality reduction, using the notion of Pareto optimality, we propose an adaptive first-ord…

SONODEs and ANODEs improve learning of second order dynamics.

Parallel computing has played an important role in speeding up convex optimization methods for big data analytics and large-scale machine learning (ML). However, the scalability of these optimization methods is inhibited by the cost of communicating and synchronizing processors in a parallel setting. Iterative ML metho…

Paper proposes a new method to measure model sensitivity using final model only.

Emulator speeds up landslide run-out modeling sensitivity analysis.

Study a continuous-time PA problem with private effort and consumption decisions.

It is an open question whether there are Vassiliev invariants that can distinguish an oriented knot from its inverse, i.e., the knot with the opposite orientation. In this article, an example is given for a first order Vassiliev invariant that takes different values on a virtual knot and its inverse. The Vassiliev inva…

With the growth of renewable generation (RG) and the development of associated ride through curves serving as operating limits, during disturbances, on violation of these limits, the power system is at risk of losing large amounts of generation. In order to identify preventive control measures that avoid such scenarios…

The paper explores how different loss functions impact reinforcement learning algorithms.

A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov trials and independent Bernoulli trials. We show that the pattern time statistics c…

With the rapid adoption of machine learning systems in sensitive applications, there is an increasing need to make black-box models explainable. Often we want to identify an influential group of training samples in a particular test prediction for a given machine learning model. Existing influence functions tackle this…

Geometric approach to thermodynamics of chemical reaction networks.

Researchers use information geometry to analyze and improve DRWs for node classification.

We address online combinatorial optimization when the player has a prior over the adversary's sequence of losses. In this framework, Russo and Van Roy proposed an information-theoretic analysis of Thompson Sampling based on the information ratio, resulting in optimal worst-case regret bounds. In this paper we introduce…

Machine learning algorithms have been increasingly deployed in critical automated decision-making systems that directly affect human lives. When these algorithms are only trained to minimize the training/test error, they could suffer from systematic discrimination against individuals based on their sensitive attributes…

NDDV estimates data point value from a single stochastic trajectory.

This paper provides a set of sensitivity analysis and activity identification results for a class of convex functions with a strong geometric structure, that we coined "mirror-stratifiable". These functions are such that there is a bijection between a primal and a dual stratification of the space into partitioning sets…

Most neural networks are trained using first-order optimization methods, which are sensitive to the parameterization of the model. Natural gradient descent is invariant to smooth reparameterizations because it is defined in a coordinate-free way, but tractable approximations are typically defined in terms of coordinate…

In the general framework of a semimartingale financial model and a utility function $U$ defined on the positive real line, we compute the first-order expansion of marginal utility-based prices with respect to a ``small'' number of random endowments. We show that this linear approximation has some important qualitative …

Paper proposes an efficient online Newton method with Nesterov's acceleration for streaming data.

Examines how first-order differential operators can be equivalently transformed.

New vector fields integrate first-order ODEs.

Study first-order locally convex Lie algebroids in Bastiani calculus.

New metric derived for robust optimization in stochastic control problems.

A new method solves complex constrained minimax problems.

A guide for solving first-order elliptic boundary value problems.

We study the out-of-sample properties of robust empirical optimization problems with smooth $φ$-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative "robustness parameter" $δ$ that controls the size of the deviations from the nominal model. Bu…

First-order ODEs linked to flat surfaces, leading to integrability.

Improved private geometric median estimation with nearly-linear time complexity.

Extends a theorem for first-order elliptic operators on manifolds.

Two classes of methods have been proposed for escaping from saddle points with one using the second-order information carried by the Hessian and the other adding the noise into the first-order information. The existing analysis for algorithms using noise in the first-order information is quite involved and hides the es…

For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the well known singularities of generic vector fields on the plane and the singularit…

A new method for machine learning updates reduces complexity and improves robustness.

Stabilizes online learning by using weighted reservoir sampling.

We consider first order expansions of convex penalized estimators in high-dimensional regression problems with random designs. Our setting includes linear regression and logistic regression as special cases. For a given penalty function $h$ and the corresponding penalized estimator $\hatβ$, we construct a quantity $η$,…

Efficient algorithm for contextual bandits with first-order guarantees.