A common way to estimate an unknown convex regression function $f_0: Ω\subset \mathbb{R}^d \rightarrow \mathbb{R}$ from a set of $n$ noisy observations is to fit a convex function that minimizes the sum of squared errors. However, this estimator is known for its tendency to overfit near the boundary of $Ω$, posing significant challenges in real-world applications. In this paper, we introduce a new estimator of $f_0$ that avoids this overfitting by minimizing a penalty on the subgradient while enforcing an upper bound $s_n$ on the sum of squared errors. The key advantage of this method is that $s_n$ can be directly estimated from the data. We establish the uniform almost sure consistency of the proposed estimator and its subgradient over $Ω$ as $n \rightarrow \infty$ and derive convergence rates. The effectiveness of our estimator is illustrated through its application to estimating waiting times in a single-server queue.

As AI inference scales to billions of queries and emerging reasoning and agentic workflows increase token demand, reliable estimates of per-query energy use are increasingly important for capacity planning, emissions accounting, and efficiency prioritization. Many public estimates are inconsistent and overstate energy use, because they extrapolate from limited benchmarks and fail to reflect efficiency gains achievable at scale. In this perspective, we introduce a bottom-up methodology to estimate the per-query energy of large-scale LLM systems based on token throughput. For models running on an H100 node under realistic workloads, GPU utilization and PUE constraints, we estimate a median energy per query of 0.34 Wh (IQR: 0.18-0.67) for frontier-scale models (>200 billion parameters). These results are consistent with measurements using production-scale configurations and show that non-production estimates and assumptions can overstate energy use by 4-20x. Extending to test-time scaling scenarios with 15x more tokens per typical query, the median energy rises 13x to 4.32 Wh, indicating that targeting efficiency in this regime will deliver the largest fleet-wide savings. We quantify achievable efficiency gains at the model, serving platform, and hardware levels, finding individual median reductions of 1.5-3.5x in energy per query, while combined advances can plausibly deliver 8-20x reductions. To illustrate the system-level impact, we estimate the baseline daily energy use of a deployment serving 1 billion queries to be 0.8 GWh/day. If 10% are long queries, demand could grow to 1.8 GWh/day. With targeted efficiency interventions, it falls to 0.9 GWh/day, similar to the energy footprint of web search at that scale. This echoes how data centers historically tempered energy growth through efficiency gains during the internet and cloud build-up.

Traffic accidents remain a major global concern, with lane-change maneuvers recognized as one of the significant contributors to collision risk. Anticipating these maneuvers has become an important research focus, supporting both traffic safety and the safe integration of autonomous and assisted driving technologies. Over the past decade, numerous models have been developed for lane-change prediction. However, most existing works have been designed and validated using simulation environments or pre-recorded datasets. While these settings allow for benchmarking and controlled evaluation, they often rely on simplified assumptions about sensing, communication, and vehicle behavior that do not fully capture the complexity of real-world operation. Real-world deployments of lane-change prediction systems are relatively rare, and when they are reported, their practical challenges, limitations, and insights remain under-documented. To illustrate the setting more concretely, consider the left lane change scenario shown in Figure 1. The Ego Vehicle (EV) is driving in the left lane, while the Target Vehicle (TV) is moving in the right lane behind a Preceding Vehicle (PV). When the PV suddenly brakes, the TV must change lanes to avoid a collision.