arXiv research

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…

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…

Deviation inequalities for stochastic approximation methods.

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

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 …

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

Adaptive model learns from time series data with changing distributions.

The paper optimizes forecasting for risk-adjusted decisions under trading frictions.

The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value. The theory is called Leptokurti…

Expectiles were defined using a minimisation principle. They form a special class of coherent risk measures. We will describe the scenario set and we will show that there is a most severe commonotonic risk measure that is smaller than the given expectile.

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

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

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

New method for PU learning with instance-dependent propensity scores.

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…

Study examines insider trading in short-selling restricted markets.

Holdout set improves risk score accuracy without biasing predictions.

Adaptive reward models capture individual preferences from human feedback.

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

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

Randomised classifiers outperform deterministic ones in strategic classification.

Portfolio optimisation typically aims to provide an optimal allocation that minimises risk, at a given return target, by diversifying over different investments. However, the potential scope of such risk diversification can be limited if investments are concentrated in only one country, or more specifically one currenc…

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

New bounds improve generalization in machine learning with high probability.

Study optimizes Bitcoin futures hedging to reduce liquidation risk.

Collider regression improves predictive performance in regression tasks.

Solves ambiguity in incomplete markets by minimizing price measure entropy.

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…

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

A method improves Cryo-EM 3D map refinement by regularizing rotation estimation.

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

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…

Study optimal consumption and investment for investors with Epstein-Zin preferences.

New method uses kernel Stein discrepancy for measure transport without strict continuity constraints.

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 …

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…

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…

Sharp stability result for maps near infinitely concentrated minimisers.

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

New results on hypersurfaces show no branch points, improving smoothness.

We study the problem of finding strain-minimising stream surfaces in a divergence-free vector field. These surfaces are generated by motions of seed curves that propagate through the field in a strain minimising manner, i.e., they move without stretching or shrinking, preserving the length of their arbitrary arc. In ge…

Loss minimisation fails to capture epistemic uncertainty in second-order predictors.

New method optimises worst-case risk under model uncertainty.

Ensuring that classifiers are non-discriminatory or fair with respect to a sensitive feature (e.g., race or gender) is a topical problem. Progress in this task requires fixing a definition of fairness, and there have been several proposals in this regard over the past few years. Several of these, however, assume either…

Let $Ω\subset \mathbb{R}^3$ be a Lipschitz domain, and consider a harmonic map $v: Ω\rightarrow \mathbb{S}^2$ with boundary data $v|\partialΩ= \varphi$ which minimises the Dirichlet energy. For $p\geq 2$, we show that any energy minimiser $u$ whose boundary map $ψ$ has a small $W^{1,p}$-distance to $\varphi$ is close t…

We prove existence and regularity of minimisers for the Canham-Helfrich energy in the class of weak (possibly branched and bubbled) immersions of the $2$-sphere. This solves (the spherical case) of the minimisation problem proposed by Helfrich in 1973, modelling lipid bilayer membranes. On the way to prove the main res…

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

An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$. This paper focuses on methods where the selection of points is essentially deterministic, with an emphasis on achi…