Under certain assumptions, frequently made for Bayes consistencyresults, we show that consistency in GeDTs and GeFs extend to any pattern of missing inputfeatures, ifmissing atrandom.

Accurate medium-range precipitation forecasting is crucial for hydrometeorological risk management and disaster mitigation, yet remains challenging for current numerical weather prediction (NWP) systems. Traditional ensemble systems such as the Global Ensemble Forecast System (GEFS) struggle to maintain high skill, especially for moderate and heavy rainfall at extended lead times. This study develops a deep learning-based ensemble framework for multi-step precipitation prediction through joint modeling of a comprehensive set of atmospheric variables. The model is trained on ERA5 reanalysis data at 0.25$^{\circ}$ spatial resolution, with precipitation labels from NASA's Integrated Multi-satellite Retrievals for Global Precipitation Measurement (GPM) constellation (IMERG), incorporating 57 input variables, including upper-air and surface predictors. The architecture employs a patch-based Swin Transformer backbone with periodic convolutions to handle longitudinal continuity and integrates time and noise embeddings through conditional layer normalization. A dual-branch decoder predicts total precipitation and other variables, with targeted freezing of encoder-decoder pathways for specialized training. Training minimizes a hybrid loss combining the Continuous Ranked Probability Score (CRPS) and weighted log1p mean squared error (log1pMSE), balancing probabilistic accuracy and magnitude fidelity. During inference, the model ingests real-time Global Forecast System (GFS) initial conditions to generate 15-day forecasts autoregressively. Evaluation against GEFS using IMERG data demonstrates higher Critical Success Index (CSI) scores at precipitation thresholds of 0.1 mm, 1 mm, 10 mm, and 20 mm, highlighting improved performance for moderate to heavy rainfall.

Then f (x) = p( Y | x), provided that p (x) > 0. Proof. Since the GeDT is deterministic, it has at most one non-zero child. Before proving Theorem 2 we need to introduce some background. We are now ready to prove Theorem 2. Proof. (see also proof of Theorem 1). Here, we assume for simplicity that all variables are continuous.

Exemplar-Free Counting aims to count objects of interest without intensive annotations of objects or exemplars. To achieve this, we propose Gated Context-Aware Swin-UNet (GCA-SUN) to directly map an input image to the density map of countable objects. Specifically, a Gated Context-Aware Modulation module is designed in the encoder to suppress irrelevant objects or background through a gate mechanism and exploit the attentive support of objects of interest through a self-similarity matrix. The gate strategy is also incorporated into the bottleneck network and the decoder to highlight the features most relevant to objects of interest. By explicitly exploiting the attentive support among countable objects and eliminating irrelevant features through the gate mechanisms, the proposed GCA-SUN focuses on and counts objects of interest without relying on predefined categories or exemplars. Experimental results on the FSC-147 and CARPK datasets demonstrate that GCA-SUN outperforms state-of-the-art methods.

Advancements in 3D Gaussian Splatting have significantly accelerated 3D reconstruction and generation. However, it may require a large number of Gaussians, which creates a substantial memory footprint. This paper introduces GES (Generalized Exponential Splatting), a novel representation that employs Generalized Exponential Function (GEF) to model 3D scenes, requiring far fewer particles to represent a scene and thus significantly outperforming Gaussian Splatting methods in efficiency with a plug-and-play replacement ability for Gaussian-based utilities. GES is validated theoretically and empirically in both principled 1D setup and realistic 3D scenes. It is shown to represent signals with sharp edges more accurately, which are typically challenging for Gaussians due to their inherent low-pass characteristics. Our empirical analysis demonstrates that GEF outperforms Gaussians in fitting natural-occurring signals (e.g. squares, triangles, and parabolic signals), thereby reducing the need for extensive splitting operations that increase the memory footprint of Gaussian Splatting. With the aid of a frequency-modulated loss, GES achieves competitive performance in novel-view synthesis benchmarks while requiring less than half the memory storage of Gaussian Splatting and increasing the rendering speed by up to 39%. The code is available on the project website https://abdullahamdi.com/ges .

Uncertainty quantification is crucial to decision-making. A prominent example is probabilistic forecasting in numerical weather prediction. The dominant approach to representing uncertainty in weather forecasting is to generate an ensemble of forecasts. This is done by running many physics-based simulations under different conditions, which is a computationally costly process. We propose to amortize the computational cost by emulating these forecasts with deep generative diffusion models learned from historical data. The learned models are highly scalable with respect to high-performance computing accelerators and can sample hundreds to tens of thousands of realistic weather forecasts at low cost. When designed to emulate operational ensemble forecasts, the generated ones are similar to physics-based ensembles in important statistical properties and predictive skill. When designed to correct biases present in the operational forecasting system, the generated ensembles show improved probabilistic forecast metrics. They are more reliable and forecast probabilities of extreme weather events more accurately. While this work demonstrates the utility of the methodology by focusing on weather forecasting, the generative artificial intelligence methodology can be extended for uncertainty quantification in climate modeling, where we believe the generation of very large ensembles of climate projections will play an increasingly important role in climate risk assessment.

Decision Trees and Random Forests are among the most widely used machine learning models, and often achieve state-of-the-art performance in tabular, domain-agnostic datasets. Nonetheless, being primarily discriminative models they lack principled methods to manipulate the uncertainty of predictions. In this paper, we exploit Generative Forests (GeFs), a recent class of deep probabilistic models that addresses these issues by extending Random Forests to generative models representing the full joint distribution over the feature space. We demonstrate that GeFs are uncertainty-aware classifiers, capable of measuring the robustness of each prediction as well as detecting out-of-distribution samples.

Decision Trees (DTs) and Random Forests (RFs) are powerful discriminative learners and tools of central importance to the everyday machine learning practitioner and data scientist. Due to their discriminative nature, however, they lack principled methods to process inputs with missing features or to detect outliers, which requires pairing them with imputation techniques or a separate generative model. In this paper, we demonstrate that DTs and RFs can naturally be interpreted as generative models, by drawing a connection to Probabilistic Circuits, a prominent class of tractable probabilistic models. This reinterpretation equips them with a full joint distribution over the feature space and leads to Generative Decision Trees (GeDTs) and Generative Forests (GeFs), a family of novel hybrid generative-discriminative models. This family of models retains the overall characteristics of DTs and RFs while additionally being able to handle missing features by means of marginalisation. Under certain assumptions, frequently made for Bayes consistency results, we show that consistency in GeDTs and GeFs extend to any pattern of missing input features, if missing at random. Empirically, we show that our models often outperform common routines to treat missing data, such as K-nearest neighbour imputation, and moreover, that our models can naturally detect outliers by monitoring the marginal probability of input features.