arXiv research

Study examines insider trading in short-selling restricted markets.

A novel optimisation framework through quadratic nonlinear projection is introduced for credit portfolio when the portfolio risk is measured by Conditional Value-at-Risk (CVaR). The whole optimisation procedure to search toward the optimal portfolio state is conducted by a series of single-step optimisations under the …

It is well known that mean-variance portfolio selection is a time-inconsistent optimal control problem in the sense that it does not satisfy Bellman's optimality principle and therefore the usual dynamic programming approach fails. We develop a time- consistent formulation of this problem, which is based on a local not…

In machine learning we often try to optimise a decision rule that would have worked well over a historical dataset; this is the so called empirical risk minimisation principle. In the context of learning from recommender system logs, applying this principle becomes a problem because we do not have available the reward …

Robust risk minimisation has several advantages: it has been studied with regards to improving the generalisation properties of models and robustness to adversarial perturbation. We bound the distributionally robust risk for a model class rich enough to include deep neural networks by a regularised empirical risk invol…

Deviation inequalities for stochastic approximation methods.

In this paper we formulate in general terms an approach to prove strong consistency of the Empirical Risk Minimisation inductive principle applied to the prototype or distance based clustering. This approach was motivated by the Divisive Information-Theoretic Feature Clustering model in probabilistic space with Kullbac…

Study robust linear regression with outliers, providing exact asymptotics for ERM performance.

RKHS-SHAP uses Shapley values for kernel methods to provide feature attributions.

Adaptive reward models capture individual preferences from human feedback.

Gradient descent performs well on weakly convex losses, offering generalization guarantees.

We present a model of predatory traders interacting with each other in the presence of a central reserve (which dissipates their wealth through say, taxation), as well as inflation. This model is examined on a network for the purposes of correlating complexity of interactions with systemic risk. We suggest the use of s…

Adaptive model learns from time series data with changing distributions.

Study shows IRM framework can be unstable with small changes, leading to worse generalization.

New method for insurance valuation combining hedging and risk minimization.

Collider regression improves predictive performance in regression tasks.

In this paper, a new approach to computing the generalisation performance is presented that assumes the distribution of risks, $ρ(r)$, for a learning scenario is known. From this, the expected error of a learning machine using empirical risk minimisation is computed for both classification and regression problems. A cr…

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules via the proper-composite representation, in which predictions are mapped to probab…

Stochastic RNNs classify biological neural network paths with robust error bounds.

Enhanced feature learning using neural networks and kernel methods with improved robustness.

Study characterizes learning from heavy-tailed data in high dimensions using superstatistical methods.

We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity, and smoothness, we establish statistical learning rates that retain, up to logari…

The paper addresses missing data imputation issues by correcting for distribution shift.

This paper introduces efficient approximations for fairness criteria in regression models.

New findings show second-order scoring rules can't accurately represent epistemic uncertainty.

Upper bounds and lower bounds show ERM outperforms DG methods in various settings.

The study characterizes learning Gaussian mixtures using GLMs in high dimensions.

The study analyzes multi-class teacher-student perceptron performance and generalization errors.

The paper analyzes fluctuations in ensemble models in high-dimensional settings.

In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for empirical risk minimizers. In the general setting, we prove sanity-check bounds in the spirit of \cite{KR99} \textquotedblleft\textit{bounds showing that the worst-case error of this estimate is not m…

Optimal convex loss function improves regression coefficient estimation.

This work studies adversarial training in high dimensions, revealing key feature trade-offs.

Analyzes deep neural networks training errors with SGD and random init.

Randomised classifiers outperform deterministic ones in strategic classification.

Deep models can fit noisy labels, but robustness and reliability are still issues.

A thesis submitted for the degree of Doctor of Philosophy of The Australian National University. In this work we introduce several new optimisation methods for problems in machine learning. Our algorithms broadly fall into two categories: optimisation of finite sums and of graph structured objectives. The finite sum pr…

New bounds improve generalization in machine learning with high probability.

The non-storability of electricity makes it unique among commodity assets, and it is an important driver of its price behaviour in secondary financial markets. The instantaneous and continuous matching of power supply with demand is a key factor explaining its volatility. During periods of high demand, costlier generat…

Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high-resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often with a pixel-wise mean squared error (MSE) loss. However, the outputs from such …

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups whic…

Every locally compact local group is locally isomorphic to a topological group.

Generalizing the notion of local $φ$-symmetry of Takahashi, in the present paper, we introduce the notion of local $φ$-semisymmetry of a Sasakian manifold along with its proper existence and characterization. We also study the notion of local Ricci (resp., projective, conformal) $φ$-semisymmetry of a Sasakian manifold …

Local Gradient Descent with local steps converges to the centralized model in the interpolation regime.

Positive simplicial volume implies locally symmetric space structure.

We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants…

We modify previous quasi-local mass definition. The new definition provides expressions of the quasi-local energy, the quasi-local linear momentum and the quasi-local mass. And they are equal to the ADM expressions at spatial infinity. Moreover, the new quasi-local energy has the positivity property.

Localized diffusion models reduce training complexity by exploiting low-dimensional structure.

Generalizes machine learning models using localization kernels and local means.