arXiv subjects

J. du Toit

Publications and source records attributed to J. du Toit.

3 recordsLinked to original sources

arXiv2026

Adaptive Two-Stage Online Learning for Service-Affecting Failure Detection in Mobile Core Networks

Mobile network operators monitor aggregated traffic volumes to assess the operational health of core network infrastructure. Reliable failure detection is challenging due to strong temporal structure, non-stationarity, measurement artefacts, and extreme class imbalance, which limit static threshold-based monitoring. This paper proposes a two-stage online learning framework for traffic-based failure detection in mobile core networks. Stage I incrementally models normal traffic dynamics using lightweight regression with time-aware features. Stage II analyses prediction residuals together with contextual indicators to detect genuine service-affecting network failures. The framework operates fully online under a prequential evaluation protocol, enabling continuous adaptation with low computational overhead. Across linear and non-linear models, the proposed two-stage architecture achieves the best precision-recall trade-off, attaining the highest recall, F1-score, and AUC at acceptable false positive rates. These results demonstrate the importance of explicit residual decomposition for reliable failure detection in streaming mobile core network data.

cs.LG↗

arXiv2007

Predicting the Last Zero of Brownian Motion with Drift

Given a standard Brownian motion $B^μ=(B_t^μ)_{0\le t\le T}$ with drift $μ\in IR$ and letting $g$ denote the last zero of $B^μ$ before $T$, we consider the optimal prediction problem V_*=\inf_{0\le τ\le T}\mathsf {E}\:|\:g-τ| where the infimum is taken over all stopping times $τ$ of $B^μ$. Reducing the optimal prediction problem to a parabolic free-boundary problem and making use of local time-space calculus techniques, we show that the following stopping time is optimal: τ_*=\inf {t\in [0,T] | B_t^μ \le b_-(t) or B_t^μ \ge b_+(t)} where the function $t\mapsto b_-(t)$ is continuous and increasing on $[0,T]$ with $b_-(T)=0$, the function $t\mapsto b_+(t)$ is continuous and decreasing on $[0,T]$ with $b_+(T)=0$, and the pair $b_-$ and $b_+$ can be characterised as the unique solution to a coupled system of nonlinear Volterra integral equations. This also yields an explicit formula for $V_*$ in terms of $b_-$ and $b_+$. If $μ=0$ then $b_-=-b_+$ and there is a closed form expression for $b_{\pm}$ as shown in [10] using the method of time change from [4]. The latter method cannot be extended to the case when $μ\ne 0$ and the present paper settles the remaining cases using a different approach.

math.PR↗

arXiv2007

The trap of complacency in predicting the maximum

Given a standard Brownian motion $B^μ=(B_t^μ)_{0\le t\le T}$ with drift $μ\in \mathbb{R}$ and letting $S_t^μ=\max_{0\le s\le t}B_s^μ$ for $0\le t\le T$, we consider the optimal prediction problem: \[V=\inf_{0\le τ\le T}\mathsf{E}(B_τ^μ-S_T^μ)^2\] where the infimum is taken over all stopping times $τ$ of $B^μ$. Reducing the optimal prediction problem to a parabolic free-boundary problem we show that the following stopping time is optimal: \[τ_*=\inf \{t_*\le t\le T\mid b_1(t)\le S_t^μ-B_t^μ\le b_2(t)\}\] where $t_*\in [0,T)$ and the functions $t\mapsto b_1(t)$ and $t\mapsto b_2(t)$ are continuous on $[t_*,T]$ with $b_1(T)=0$ and $b_2(T)=1/2μ$. If $μ>0$, then $b_1$ is decreasing and $b_2$ is increasing on $[t_*,T]$ with $b_1(t_*)=b_2(t_*)$ when $t_*\ne 0$. Using local time-space calculus we derive a coupled system of nonlinear Volterra integral equations of the second kind and show that the pair of optimal boundaries $b_1$ and $b_2$ can be characterized as the unique solution to this system. This also leads to an explicit formula for $V$ in terms of $b_1$ and $b_2$. If $μ\le 0$, then $t_*=0$ and $b_2\equiv +\infty$ so that $τ_*$ is expressed in terms of $b_1$ only. In this case $b_1$ is decreasing on $[z_*,T]$ and increasing on $[0,z_*)$ for some $z_*\in [0,T)$ with $z_*=0$ if $μ=0$, and the system of two Volterra equations reduces to one Volterra equation. If $μ=0$, then there is a closed form expression for $b_1$. This problem was solved in [Theory Probab. Appl. 45 (2001) 125--136] using the method of time change (i.e., change of variables). The method of time change cannot be extended to the case when $μ\ne 0$ and the present paper settles the remaining cases using a different approach.

math.PR↗