Abstract--Characterizing application-layer user throughput in next-generation networks is increasingly challenging as the higher capacity of the 5G Radio Access Network (RAN) shifts connectivity bottlenecks towards deeper parts of the network. Traditional methods, such as drive tests and operator equipment counters, are costly, limited, or fail to capture end-to-end (E2E) Quality of Service (QoS) and its variability. In this work, we leverage large-scale crowdsourced measurements--including E2E, radio, contextual and network deployment features collected by the user equipment (UE)--to propose an uncertainty-aware and explainable approach for downlink user throughput estimation. T o address the variability of throughput, we apply NGBoost, a model that outputs both point estimates and calibrated confidence intervals, representing its first use in the field of computer communications. Finally, we use the proposed model to analyze the evolution from 4G to 5G SA, and show that throughput bottlenecks move from the RAN to transport and service layers, as seen by E2E metrics gaining importance over radio-related features. Over the past two decades, the widespread adoption of mobile broadband networks has intensified both user and industry demands for reliable and predictable Quality of Service (QoS) to support effective network management and optimization. Among QoS indicators, user throughput is a primary concern for bandwidth-intensive applications such as media streaming and large file transfers.

Regression under uncertainty is fundamental across science and engineering. We present an Anchored Mixture of Experts (Anchor-MoE), a model that handles both probabilistic and point regression. For simplicity, we use a tuned gradient-boosting model to furnish the anchor mean; however, any off-the-shelf point regressor can serve as the anchor. The anchor prediction is projected into a latent space, where a learnable metric-window kernel scores locality and a soft router dispatches each sample to a small set of mixture-density-network experts; the experts produce a heteroscedastic correction and predictive variance. We train by minimizing negative log-likelihood, and on a disjoint calibration split fit a post-hoc linear map on predicted means to improve point accuracy. On the theory side, assuming a Hölder smooth regression function of order~$α$ and fixed Lipschitz partition-of-unity weights with bounded overlap, we show that Anchor-MoE attains the minimax-optimal $L^2$ risk rate $O\!\big(N^{-2α/(2α+d)}\big)$. In addition, the CRPS test generalization gap scales as $\widetilde{O}\!\Big(\sqrt{(\log(Mh)+P+K)/N}\Big)$; it is logarithmic in $Mh$ and scales as the square root in $P$ and $K$. Under bounded-overlap routing, $K$ can be replaced by $k$, and any dependence on a latent dimension is absorbed into $P$. Under uniformly bounded means and variances, an analogous $\widetilde{O}\!\big(\sqrt{(\log(Mh)+P+K)/N}\big)$ scaling holds for the test NLL up to constants. Empirically, across standard UCI regressions, Anchor-MoE consistently matches or surpasses the strong NGBoost baseline in RMSE and NLL; on several datasets it achieves new state-of-the-art probabilistic regression results on our benchmark suite. Code is available at https://github.com/BaozhuoSU/Probabilistic_Regression.

PV power forecasting models are predominantly based on machine learning algorithms which do not provide any insight into or explanation about their predictions (black boxes). Therefore, their direct implementation in environments where transparency is required, and the trust associated with their predictions may be questioned. To this end, we propose a two stage probabilistic forecasting framework able to generate highly accurate, reliable, and sharp forecasts yet offering full transparency on both the point forecasts and the prediction intervals (PIs). In the first stage, we exploit natural gradient boosting (NGBoost) for yielding probabilistic forecasts, while in the second stage, we calculate the Shapley additive explanation (SHAP) values in order to fully comprehend why a prediction was made. To highlight the performance and the applicability of the proposed framework, real data from two PV parks located in Southern Germany are employed. Comparative results with two state-of-the-art algorithms, namely Gaussian process and lower upper bound estimation, manifest a significant increase in the point forecast accuracy and in the overall probabilistic performance. Most importantly, a detailed analysis of the model's complex nonlinear relationships and interaction effects between the various features is presented. This allows interpreting the model, identifying some learned physical properties, explaining individual predictions, reducing the computational requirements for the training without jeopardizing the model accuracy, detecting possible bugs, and gaining trust in the model. Finally, we conclude that the model was able to develop complex nonlinear relationships which follow known physical properties as well as human logic and intuition.

Gradient-boosted regression trees (GBRTs) are hugely popular for solving tabular regression problems, but provide no estimate of uncertainty. We propose Instance-Based Uncertainty estimation for Gradient-boosted regression trees (IBUG), a simple method for extending any GBRT point predictor to produce probabilistic predictions. IBUG computes a non-parametric distribution around a prediction using the $k$-nearest training instances, where distance is measured with a tree-ensemble kernel. The runtime of IBUG depends on the number of training examples at each leaf in the ensemble, and can be improved by sampling trees or training instances. Empirically, we find that IBUG achieves similar or better performance than the previous state-of-the-art across 22 benchmark regression datasets. We also find that IBUG can achieve improved probabilistic performance by using different base GBRT models, and can more flexibly model the posterior distribution of a prediction than competing methods. We also find that previous methods suffer from poor probabilistic calibration on some datasets, which can be mitigated using a scalar factor tuned on the validation data. Source code is available at https://www.github.com/jjbrophy47/ibug.

Sequential model-based optimization sequentially selects a candidate point by constructing a surrogate model with the history of evaluations, to solve a black-box optimization problem. Gaussian process (GP) regression is a popular choice as a surrogate model, because of its capability of calculating prediction uncertainty analytically. On the other hand, an ensemble of randomized trees is another option and has practical merits over GPs due to its scalability and easiness of handling continuous/discrete mixed variables. In this paper we revisit various ensembles of randomized trees to investigate their behavior in the perspective of prediction uncertainty estimation. Then, we propose a new way of constructing an ensemble of randomized trees, referred to as BwO forest, where bagging with oversampling is employed to construct bootstrapped samples that are used to build randomized trees with random splitting. Experimental results demonstrate the validity and good performance of BwO forest over existing tree-based models in various circumstances.

PyCaret is an open-source, low-code machine learning library and end-to-end model management tool built-in Python for automating machine learning workflows. It is incredibly popular for its ease of use, simplicity, and ability to quickly and efficiently build and deploy end-to-end ML prototypes. PyCaret is an alternate low-code library that can replace hundreds of code lines with few lines only. This makes the experiment cycle exponentially fast and efficient. PyCaret is simple and easy to use.

Many single-target regression problems require estimates of uncertainty along with the point predictions. Probabilistic regression algorithms are well-suited for these tasks. However, the options are much more limited when the prediction target is multivariate and a joint measure of uncertainty is required. For example, in predicting a 2D velocity vector a joint uncertainty would quantify the probability of any vector in the plane, which would be more expressive than two separate uncertainties on the x- and y- components. To enable joint probabilistic regression, we propose a Natural Gradient Boosting (NGBoost) approach based on nonparametrically modeling the conditional parameters of the multivariate predictive distribution. Our method is robust, works out-of-the-box without extensive tuning, is modular with respect to the assumed target distribution, and performs competitively in comparison to existing approaches. We demonstrate these claims in simulation and with a case study predicting two-dimensional oceanographic velocity data. An implementation of our method is available at https://github.com/stanfordmlgroup/ngboost.

PyCaret is an open-source, low-code machine learning library and end-to-end model management tool built-in Python for automating machine learning workflows. It is incredibly popular for its ease of use, simplicity, and ability to quickly and efficiently build and deploy end-to-end ML prototypes. PyCaret is an alternate low-code library that can replace hundreds of code lines with few lines only. This makes the experiment cycle exponentially fast and efficient. PyCaret is simple and easy to use.