Deep Reinforcement Learning (DRL) has demonstrated potential in addressing robotic local planning problems, yet its efficacy remains constrained in highly unstructured and dynamic environments. To address these challenges, this study proposes the ColorDynamic framework. First, an end-to-end DRL formulation is established, which maps raw sensor data directly to control commands, thereby ensuring compatibility with unstructured environments. Under this formulation, a novel network, Transqer, is introduced. The Transqer enables online DRL learning from temporal transitions, substantially enhancing decision-making in dynamic scenarios. To facilitate scalable training of Transqer with diverse data, an efficient simulation platform E-Sparrow, along with a data augmentation technique leveraging symmetric invariance, are developed. Comparative evaluations against state-of-the-art methods, alongside assessments of generalizability, scalability, and real-time performance, were conducted to validate the effectiveness of ColorDynamic. Results indicate that our approach achieves a success rate exceeding 90% while exhibiting real-time capacity (1.2-1.3 ms per planning). Additionally, ablation studies were performed to corroborate the contributions of individual components. Building on this, the OkayPlan-ColorDynamic (OPCD) navigation system is presented, with simulated and real-world experiments demonstrating its superiority and applicability in complex scenarios. The codebase and experimental demonstrations have been open-sourced on our website to facilitate reproducibility and further research.

This work proposes a scalable probabilistic latent variable model based on Gaussian processes (Lawrence, 2004) in the context of multiple observation spaces. We focus on an application in astrophysics where data sets typically contain both observed spectral features and scientific properties of astrophysical objects such as galaxies or exoplanets. In our application, we study the spectra of very luminous galaxies known as quasars, along with their properties, such as the mass of their central supermassive black hole, accretion rate, and luminosity-resulting in multiple observation spaces. A single data point is then characterized by different classes of observations, each with different likelihoods. Our proposed model extends the baseline stochastic variational Gaussian process latent variable model (GPLVM) introduced by Lalchand et al. (2022) to this setting, proposing a seamless generative model where the quasar spectra and scientific labels can be generated simultaneously using a shared latent space as input to different sets of Gaussian process decoders, one for each observation space. Additionally, this framework enables training in a missing data setting where a large number of dimensions per data point may be unknown or unobserved. We demonstrate high-fidelity reconstructions of the spectra and scientific labels during test-time inference and briefly discuss the scientific interpretations of the results, along with the significance of such a generative model.

In this paper we present the results of an experiment aimed to use machine learning methods to obtain models that can be used for the automatic classification of products. In order to apply automatic classification methods, we transformed the product names from a text representation to numeric vectors, a process called word embedding. We used several embedding methods: Count Vectorization, TF-IDF, Word2Vec, FASTTEXT, and GloVe. Having the product names in a form of numeric vectors, we proceeded with a set of machine learning methods for automatic classification: Logistic Regression, Multinomial Naive Bayes, kNN, Artificial Neural Networks, Support Vector Machines, and Decision trees with several variants. The results show an impressive accuracy of the classification process for Support Vector Machines, Logistic Regression, and Random Forests. Regarding the word embedding methods, the best results were obtained with the FASTTEXT technique.

Information-theoretic quantities play a crucial role in understanding non-linear relationships between random variables and are widely used across scientific disciplines. However, estimating these quantities remains an open problem, particularly in the case of high-dimensional discrete distributions. Current approaches typically rely on embedding discrete data into a continuous space and applying neural estimators originally designed for continuous distributions, a process that may not fully capture the discrete nature of the underlying data. We consider Continuous-Time Markov Chains (CTMCs), stochastic processes on discrete state-spaces which have gained popularity due to their generative modeling applications. In this work, we introduce INFO-SEDD, a novel method for estimating information-theoretic quantities of discrete data, including mutual information and entropy. Our approach requires the training of a single parametric model, offering significant computational and memory advantages. Additionally, it seamlessly integrates with pretrained networks, allowing for efficient reuse of pretrained generative models. To evaluate our approach, we construct a challenging synthetic benchmark. Our experiments demonstrate that INFO-SEDD is robust and outperforms neural competitors that rely on embedding techniques. Moreover, we validate our method on a real-world task: estimating the entropy of an Ising model. Overall, INFO-SEDD outperforms competing methods and shows scalability to high-dimensional scenarios, paving the way for new applications where estimating MI between discrete distribution is the focus. The promising results in this complex, high-dimensional scenario highlight INFO-SEDD as a powerful new estimator in the toolkit for information-theoretical analysis.

We have derived a novel loss function from the Fokker-Planck equation that links dynamical system models with their probability density functions, demonstrating its utility in model identification and density estimation. In the first application, we show that this loss function can enable the extraction of dynamical parameters from non-temporal datasets, including timestamp-free measurements from steady non-equilibrium systems such as noisy Lorenz systems and gene regulatory networks. In the second application, when coupled with a density estimator, this loss facilitates density estimation when the dynamic equations are known. For density estimation, we propose a density estimator that integrates a Gaussian Mixture Model with a normalizing flow model. It simultaneously estimates normalized density, energy, and score functions from both empirical data and dynamics. It is compatible with a variety of data-based training methodologies, including maximum likelihood and score matching. It features a latent space akin to a modern Hopfield network, where the inherent Hopfield energy effectively assigns low densities to sparsely populated data regions, addressing common challenges in neural density estimators. Additionally, this Hopfield-like energy enables direct and rapid data manipulation through the Concave-Convex Procedure (CCCP) rule, facilitating tasks such as denoising and clustering. Our work demonstrates a principled framework for leveraging the complex interdependencies between dynamics and density estimation, as illustrated through synthetic examples that clarify the underlying theoretical intuitions.

We study two G-modeling strategies for estimating the signal distribution (the empirical Bayesian's prior) from observations corrupted with normal noise. First, we choose the signal distribution by minimizing Stein's unbiased risk estimate (SURE) of the implied Eddington/Tweedie Bayes denoiser, an approach motivated by optimal empirical Bayesian shrinkage estimation of the signals. Second, we select the signal distribution by minimizing Hyv\"arinen's score matching objective for the implied score (derivative of log-marginal density), targeting minimal Fisher divergence between estimated and true marginal densities. While these strategies appear distinct, they are known to be mathematically equivalent. We provide a unified analysis of SURE and score matching under both well-specified signal distribution classes and misspecification. In the classical well-specified setting with homoscedastic noise and compactly supported signal distribution, we establish nearly parametric rates of convergence of the empirical Bayes regret and the Fisher divergence. In a commonly studied misspecified model, we establish fast rates of convergence to the oracle denoiser and corresponding oracle inequalities. Our empirical results demonstrate competitiveness with nonparametric maximum likelihood in well-specified settings, while showing superior performance under misspecification, particularly in settings involving heteroscedasticity and side information.

Bayesian computation has achieved profound success in many modeling tasks with statistics tools such as generalized linear models (Dobson and Barnett, 2018; Nelder and Wedderburn, 1972). Yet these traditional tools fail to produce satisfactory predictions for high-dimensional and highly complex data such as images, speech and videos. Deep Learning (LeCun et al., 2015a) provides an attractive solution. At the time of late 2023, deep neural networks achieve accurate predictions for image classification (Dehghani et al., 2023), segmentation (Kirillov et al., 2023) and speech recognition tasks (Zhang et al., 2023). Meanwhile they have also demonstrated an astonishing capability for generating photo-realistic and/or artistic images (Rombach et al., 2022), music (Agostinelli et al., 2023) and videos (Liang et al., 2022). Nowadays deep neural networks have become a standard modeling tool for many of the applications in AI and related fields, and the success of deep learning so far are based on training deterministic deep neural networks on big data. So one might ask: is there a place for Bayesian computation in modern deep learning?

Recent studies have shown that Transformers can perform in-context reinforcement learning (RL) by imitating existing RL algorithms, enabling sample-efficient adaptation to unseen tasks without parameter updates. However, these models also inherit the suboptimal behaviors of the RL algorithms they imitate. This issue primarily arises due to the gradual update rule employed by those algorithms. Model-based planning offers a promising solution to this limitation by allowing the models to simulate potential outcomes before taking action, providing an additional mechanism to deviate from the suboptimal behavior. Rather than learning a separate dynamics model, we propose Distillation for In-Context Planning (DICP), an in-context model-based RL framework where Transformers simultaneously learn environment dynamics and improve policy in-context. We evaluate DICP across a range of discrete and continuous environments, including Darkroom variants and Meta-World. Our results show that DICP achieves state-of-the-art performance while requiring significantly fewer environment interactions than baselines, which include both model-free counterparts and existing meta-RL methods. Since the introduction of Transformers (V aswani et al., 2017), their versatility in handling diverse tasks has been widely recognized across various domains (Brown et al., 2020; Dosovitskiy et al., 2021; Bubeck et al., 2023). A key aspect of their success is in-context learning (Brown et al., 2020), which enables models to acquire knowledge rapidly without explicit parameter updates through gradient descent. Recently, this capability has been explored in reinforcement learning (RL) (Chen et al., 2021; Schulman et al., 2017; Lee et al., 2022; Reed et al., 2022), where acquiring skills in a sample-efficient manner is crucial. This line of research naturally extends to meta-RL, which focuses on leveraging prior knowledge to quickly adapt to novel tasks. In this context, Laskin et al. (2023) introduce Algorithm Distillation (AD), an in-context RL approach where Transformers sequentially model the entire learning histories of a specific RL algorithm across various tasks. The goal is for the models to replicate the exploration-exploitation behaviors of the source RL algorithm, enabling them to tackle novel tasks purely in-context.

This paper introduce the Python package Sparklen (see Lacoste (2025)), which implements a complete set of statistical learning methods for exponential Hawkes processes with an emphasize on high-dimension setting. Hawkes processes, introduced in Hawkes (1971), form a specific but rather versatile class of point processes. Such processes model time series in which the occurrence of one event temporarily increases the probability of other events occurring. This intrinsic ability to take into account self-exciting effects makes them particularly interesting for real data modeling. Historically applied in seismology (see Ogata (1988)), they have since been used in a wide variety of other fields, including neuroscience in Reynaud-Bouret, Rivoirard, and Tuleau-Malot (2013), finance in Bacry, Mastromatteo, and Muzy (2015), ecology in Denis, Dion-Blanc, Lacoste, Sansonnet, and Bas (2024). The multidimensional version, known as the Multivariate Hawkes Processes (MHP), captures additionally interactions among each univariate process within a network. This generalization enables the modeling of more intricate dynamics, significantly expanding the range of potential applications. For example, MHP has been applied to model action potentials within neural networks in Bonnet, Dion-Blanc, Gindraud, and Lemler (2022), or for trend detection in social networks in Pinto, Chahed, and Altman (2015).

This paper addresses the problem of satellite inspection, where one or more satellites (inspectors) are tasked with imaging or inspecting a resident space object (RSO) due to potential malfunctions or anomalies. Inspection strategies are often reduced to a discretized action space with predefined waypoints, facilitating tractability in both classical optimization and machine learning based approaches. However, this discretization can lead to suboptimal guidance in certain scenarios. This study presents a comparative simulation to explore the tradeoffs of passive versus active strategies in multi-agent missions. Key factors considered include RSO dynamic mode, state uncertainty, unmodeled entrance criteria, and inspector motion types. The evaluation is conducted with a focus on fuel utilization and surface coverage. Building on a Monte-Carlo based evaluator of passive strategies and a reinforcement learning framework for training active inspection policies, this study investigates conditions under which passive strategies, such as Natural Motion Circumnavigation (NMC), may perform comparably to active strategies like Reinforcement Learning based waypoint transfers.