We present a novel algorithm for real-time planar semantic mapping tailored for humanoid robots navigating complex terrains such as staircases. Our method is adaptable to any odometry input and leverages GPU-accelerated processes for planar extraction, enabling the rapid generation of globally consistent semantic maps. We utilize an anisotropic diffusion filter on depth images to effectively minimize noise from gradient jumps while preserving essential edge details, enhancing normal vector images' accuracy and smoothness. Both the anisotropic diffusion and the RANSAC-based plane extraction processes are optimized for parallel processing on GPUs, significantly enhancing computational efficiency. Our approach achieves real-time performance, processing single frames at rates exceeding $30~Hz$, which facilitates detailed plane extraction and map management swiftly and efficiently. Extensive testing underscores the algorithm's capabilities in real-time scenarios and demonstrates its practical application in humanoid robot gait planning, significantly improving its ability to navigate dynamic environments.

Post-translational modifications (PTMs) profoundly expand the complexity and functionality of the proteome, regulating protein attributes and interactions that are crucial for biological processes. Accurately predicting PTM sites and their specific types is therefore essential for elucidating protein function and understanding disease mechanisms. Existing computational approaches predominantly focus on protein sequences to predict PTM sites, driven by the recognition of sequence-dependent motifs. However, these approaches often overlook protein structural contexts. In this work, we first compile a large-scale sequence-structure PTM dataset, which serves as the foundation for fair comparison. We introduce the MeToken model, which tokenizes the micro-environment of each amino acid, integrating both sequence and structural information into unified discrete tokens. This model not only captures the typical sequence motifs associated with PTMs but also leverages the spatial arrangements dictated by protein tertiary structures, thus providing a holistic view of the factors influencing PTM sites. Designed to address the long-tail distribution of PTM types, MeToken employs uniform sub-codebooks that ensure even the rarest PTMs are adequately represented and distinguished. We validate the effectiveness and generalizability of MeToken across multiple datasets, demonstrating its superior performance in accurately identifying PTM types. The results underscore the importance of incorporating structural data and highlight MeToken's potential in facilitating accurate and comprehensive PTM predictions, which could significantly impact proteomics research. The code and datasets are available at https://github.com/A4Bio/MeToken.

Accurate annotation of educational resources is critical in the rapidly advancing field of online education due to the complexity and volume of content. Existing classification methods face challenges with semantic overlap and distribution imbalance of labels in the multi-label context, which impedes effective personalized learning and resource recommendation. This paper introduces RR2QC, a novel Retrieval Reranking method To multi-label Question Classification by leveraging label semantics and meta-label refinement. Firstly, RR2QC leverages semantic relationships within and across label groups to enhance pre-training strategie in multi-label context. Next, a class center learning task is introduced, integrating label texts into downstream training to ensure questions consistently align with label semantics, retrieving the most relevant label sequences. Finally, this method decomposes labels into meta-labels and trains a meta-label classifier to rerank the retrieved label sequences. In doing so, RR2QC enhances the understanding and prediction capability of long-tail labels by learning from meta-labels frequently appearing in other labels. Addtionally, a Math LLM is used to generate solutions for questions, extracting latent information to further refine the model's insights. Experimental results demonstrate that RR2QC outperforms existing classification methods in Precision@k and F1 scores across multiple educational datasets, establishing it as a potent enhancement for online educational content utilization.

A common way to drive progress of AI models and agents is to compare their performance on standardized benchmarks. Comparing the performance of general agents requires aggregating their individual performances across a potentially wide variety of different tasks. In this paper, we describe a novel ranking scheme inspired by social choice frameworks, called Soft Condorcet Optimization (SCO), to compute the optimal ranking of agents: the one that makes the fewest mistakes in predicting the agent comparisons in the evaluation data. This optimal ranking is the maximum likelihood estimate when evaluation data (which we view as votes) are interpreted as noisy samples from a ground truth ranking, a solution to Condorcet's original voting system criteria. SCO ratings are maximal for Condorcet winners when they exist, which we show is not necessarily true for the classical rating system Elo. We propose three optimization algorithms to compute SCO ratings and evaluate their empirical performance. When serving as an approximation to the Kemeny-Young voting method, SCO rankings are on average 0 to 0.043 away from the optimal ranking in normalized Kendall-tau distance across 865 preference profiles from the PrefLib open ranking archive. In a simulated noisy tournament setting, SCO achieves accurate approximations to the ground truth ranking and the best among several baselines when 59\% or more of the preference data is missing. Finally, SCO ranking provides the best approximation to the optimal ranking, measured on held-out test sets, in a problem containing 52,958 human players across 31,049 games of the classic seven-player game of Diplomacy.

In causal inference, many estimands of interest can be expressed as a linear functional of the outcome regression function; this includes, for example, average causal effects of static, dynamic and stochastic interventions. For learning such estimands, in this work, we propose novel debiased machine learning estimators that are doubly robust asymptotically linear, thus providing not only doubly robust consistency but also facilitating doubly robust inference (e.g., confidence intervals and hypothesis tests). To do so, we first establish a key link between calibration, a machine learning technique typically used in prediction and classification tasks, and the conditions needed to achieve doubly robust asymptotic linearity. We then introduce calibrated debiased machine learning (C-DML), a unified framework for doubly robust inference, and propose a specific C-DML estimator that integrates cross-fitting, isotonic calibration, and debiased machine learning estimation. A C-DML estimator maintains asymptotic linearity when either the outcome regression or the Riesz representer of the linear functional is estimated sufficiently well, allowing the other to be estimated at arbitrarily slow rates or even inconsistently. We propose a simple bootstrap-assisted approach for constructing doubly robust confidence intervals. Our theoretical and empirical results support the use of C-DML to mitigate bias arising from the inconsistent or slow estimation of nuisance functions.

Rahimi and Recht [31] introduced the idea of decomposing shift-invariant kernels by randomly sampling from their spectral distribution. This famous technique, known as Random Fourier Features (RFF), is in principle applicable to any shift-invariant kernel whose spectral distribution can be identified and simulated. In practice, however, it is usually applied to the Gaussian kernel because of its simplicity, since its spectral distribution is also Gaussian. Clearly, simple spectral sampling formulas would be desirable for broader classes of kernel functions. In this paper, we propose to decompose spectral kernel distributions as a scale mixture of $\alpha$-stable random vectors. This provides a simple and ready-to-use spectral sampling formula for a very large class of multivariate shift-invariant kernels, including exponential power kernels, generalized Mat\'ern kernels, generalized Cauchy kernels, as well as newly introduced kernels such as the Beta, Kummer, and Tricomi kernels. In particular, we show that the spectral densities of all these kernels are scale mixtures of the multivariate Gaussian distribution. This provides a very simple way to modify existing Random Fourier Features software based on Gaussian kernels to cover a much richer class of multivariate kernels. This result has broad applications for support vector machines, kernel ridge regression, Gaussian processes, and other kernel-based machine learning techniques for which the random Fourier features technique is applicable.

We propose a general framework for deriving generalization bounds for parallel positively homogeneous neural networks--a class of neural networks whose input-output map decomposes as the sum of positively homogeneous maps. Examples of such networks include matrix factorization and sensing, single-layer multi-head attention mechanisms, tensor factorization, deep linear and ReLU networks, and more. Our general framework is based on linking the non-convex empirical risk minimization (ERM) problem to a closely related convex optimization problem over prediction functions, which provides a global, achievable lower-bound to the ERM problem. We exploit this convex lower-bound to perform generalization analysis in the convex space while controlling the discrepancy between the convex model and its non-convex counterpart. We apply our general framework to a wide variety of models ranging from low-rank matrix sensing, to structured matrix sensing, two-layer linear networks, two-layer ReLU networks, and single-layer multi-head attention mechanisms, achieving generalization bounds with a sample complexity that scales almost linearly with the network width.

We give a fast, spectral procedure for implementing approximate-message passing (AMP) algorithms robustly. For any quadratic optimization problem over symmetric matrices $X$ with independent subgaussian entries, and any separable AMP algorithm $\mathcal A$, our algorithm performs a spectral pre-processing step and then mildly modifies the iterates of $\mathcal A$. If given the perturbed input $X + E \in \mathbb R^{n \times n}$ for any $E$ supported on a $\varepsilon n \times \varepsilon n$ principal minor, our algorithm outputs a solution $\hat v$ which is guaranteed to be close to the output of $\mathcal A$ on the uncorrupted $X$, with $\|\mathcal A(X) - \hat v\|_2 \le f(\varepsilon) \|\mathcal A(X)\|_2$ where $f(\varepsilon) \to 0$ as $\varepsilon \to 0$ depending only on $\varepsilon$.

This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a fixed point algorithm and a Riemannian optimization method based on the derived information geometry of Elliptical Wishart distributions. The existence and uniqueness of the MLE are characterized as well as the convergence of both estimation algorithms. Statistical properties of the MLE are also investigated such as consistency, asymptotic normality and an intrinsic version of Fisher efficiency. On the statistical learning side, novel classification and clustering methods are designed. For the $t$-Wishart distribution, the performance of the MLE and statistical learning algorithms are evaluated on both simulated and real EEG and hyperspectral data, showcasing the interest of our proposed methods.

In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture models, which are not inherently spherical but only conditionally so. Specifically, the conditional probability distribution, given a random parameter of the random vector, follows a Gaussian distribution, allowing us to apply Bayesian analysis tools to the probability function. This assumption, together with spherical radial decomposition for Gaussian random vectors, enables us to represent the probability function as an integral over the Euclidean sphere. Using this representation, we establish sufficient conditions to ensure the differentiability of the probability function and provide and integral representation of its gradient. Furthermore, leveraging the Bayesian decomposition, we approximate the probability function using random sampling over the parameter space and the Euclidean sphere. Finally, we present numerical examples that illustrate the advantages of this approach over classical approximations based on random vector sampling.