Wearable laser scanning (WLS) system has the advantages of flexibility and portability. It can be used for determining the user's path within a prior map, which is a huge demand for applications in pedestrian navigation, collaborative mapping, augmented reality, and emergency rescue. However, existing LiDAR-based global localization methods suffer from insufficient robustness, especially in complex large-scale outdoor scenes with insufficient features and incomplete coverage of the prior map. To address such challenges, we propose LiDAR-based reliable global localization (Reliable-loc) exploiting the verifiable cues in the sequential LiDAR data. First, we propose a Monte Carlo Localization (MCL) based on spatially verifiable cues, utilizing the rich information embedded in local features to adjust the particles' weights hence avoiding the particles converging to erroneous regions. Second, we propose a localization status monitoring mechanism guided by the sequential pose uncertainties and adaptively switching the localization mode using the temporal verifiable cues to avoid the crash of the localization system. To validate the proposed Reliable-loc, comprehensive experiments have been conducted on a large-scale heterogeneous point cloud dataset consisting of high-precision vehicle-mounted mobile laser scanning (MLS) point clouds and helmet-mounted WLS point clouds, which cover various street scenes with a length of over 20km. The experimental results indicate that Reliable-loc exhibits high robustness, accuracy, and efficiency in large-scale, complex street scenes, with a position accuracy of 1.66m, yaw accuracy of 3.09 degrees, and achieves real-time performance. For the code and detailed experimental results, please refer to https://github.com/zouxianghong/Reliable-loc.

In standard RL, a learner attempts to learn an optimal policy for a Markov Decision Process whose structure (e.g. state space) is known. In online model selection, a learner attempts to learn an optimal policy for an MDP knowing only that it belongs to one of $M >1$ model classes of varying complexity. Recent results have shown that this can be feasibly accomplished in episodic online RL. In this work, we propose $\mathsf{MRBEAR}$, an online model selection algorithm for the average reward RL setting. The regret of the algorithm is in $\tilde O(M C_{m^*}^2 \mathsf{B}_{m^*}(T,\delta))$ where $C_{m^*}$ represents the complexity of the simplest well-specified model class and $\mathsf{B}_{m^*}(T,\delta)$ is its corresponding regret bound. This result shows that in average reward RL, like the episodic online RL, the additional cost of model selection scales only linearly in $M$, the number of model classes. We apply $\mathsf{MRBEAR}$ to the interaction between a learner and an opponent in a two-player simultaneous general-sum repeated game, where the opponent follows a fixed unknown limited memory strategy. The learner's goal is to maximize its utility without knowing the opponent's utility function. The interaction is over $T$ rounds with no episode or discounting which leads us to measure the learner's performance by average reward regret. In this application, our algorithm enjoys an opponent-complexity-dependent regret in $\tilde O(M(\mathsf{sp}(h^*) B^{m^*} A^{m^*+1})^{\frac{3}{2}} \sqrt{T})$, where $m^*\le M$ is the unknown memory limit of the opponent, $\mathsf{sp}(h^*)$ is the unknown span of optimal bias induced by the opponent, and $A$ and $B$ are the number of actions for the learner and opponent respectively. We also show that the exponential dependency on $m^*$ is inevitable by proving a lower bound on the learner's regret.

As a key task in machine learning, data classification is essentially to find a suitable coordinate system to represent data features of different classes of samples. This paper proposes the mutual-energy inner product optimization method for constructing a feature coordinate system. First, by analyzing the solution space and eigenfunctions of partial differential equations describing a non-uniform membrane, the mutual-energy inner product is defined. Second, by expressing the mutual-energy inner product as a series of eigenfunctions, it shows a significant advantage of enhancing low-frequency features and suppressing high-frequency noise, compared with the Euclidean inner product. And then, a mutual-energy inner product optimization model is built to extract data features, and convexity and concavity properties of its objective function are discussed. Next, by combining the finite element method, a stable and efficient sequential linearization algorithm is constructed to solve the optimization model. This algorithm only solves equations including positive definite symmetric matrix and linear programming with a few constraints, and its vectorized implementation is discussed. Finally, the mutual-energy inner product optimization method is used to construct feature coordinates, and multi-class Gaussian classifiers are trained on the MINST training set. Good prediction results of Gaussian classifiers are achieved on the MINST test set.

Large Language Models (LLMs) are highly resource-intensive to fine-tune due to their enormous size. While low-rank adaptation is a prominent parameter-efficient fine-tuning approach, it suffers from sensitivity to hyperparameter choices, leading to instability in model performance on fine-tuning downstream tasks. This paper highlights the importance of effective parameterization in low-rank fine-tuning to reduce estimator variance and enhance the stability of final model outputs. We propose MonteCLoRA, an efficient fine-tuning technique, employing Monte Carlo estimation to learn an unbiased posterior estimation of low-rank parameters with low expected variance, which stabilizes fine-tuned LLMs with only O(1) additional parameters. MonteCLoRA shows significant improvements in accuracy and robustness, achieving up to 3.8% higher accuracy and 8.6% greater robustness than existing efficient fine-tuning methods on natural language understanding tasks with pre-trained RoBERTa-base. Furthermore, in generative tasks with pre-trained LLaMA-1-7B, MonteCLoRA demonstrates robust zero-shot performance with 50% lower variance than the contemporary efficient fine-tuning methods. The theoretical and empirical results presented in the paper underscore how parameterization and hyperpriors balance exploration-exploitation in the low-rank parametric space, therefore leading to more optimal and robust parameter estimation during efficient fine-tuning.

Dictionary learning (Rubinstein require capturing complex relations between et al., 2010) is a representation learning framework variables. We define a novel Graph-which aims to recover a finite set of atoms, called a Dictionary signal model, where a finite set dictionary, that can encode data through sparse coefficients. of graphs characterizes relationships in data On the other hand, graphs provide a natural distribution through a weighted sum of their representation of structured data with pairwise relationships, Laplacians. We propose a framework to infer described by edges between nodes. However, the graph dictionary representation from these relationships are often hidden, and we must infer observed data, along with a bilinear generalization them from data. of the primal-dual splitting algorithm to solve the learning problem. Our new formulation In this work, we introduce a novel Graph-Dictionary allows to include a priori knowledge signal model, GraphDict in short, to jointly address the on signal properties, as well as on underlying representation and the structure learning problems.

Bayes' rule naturally allows for inference refinement in a streaming fashion, without the need to recompute posteriors from scratch whenever new data arrives. In principle, Bayesian streaming is straightforward: we update our prior with the available data and use the resulting posterior as a prior when processing the next data chunk. In practice, however, this recipe entails i) approximating an intractable posterior at each time step; and ii) encapsulating results appropriately to allow for posterior propagation. For continuous state spaces, variational inference (VI) is particularly convenient due to its scalability and the tractability of variational posteriors. For discrete state spaces, however, state-of-the-art VI results in analytically intractable approximations that are ill-suited for streaming settings. To enable streaming Bayesian inference over discrete parameter spaces, we propose streaming Bayes GFlowNets (abbreviated as SB-GFlowNets) by leveraging the recently proposed GFlowNets -- a powerful class of amortized samplers for discrete compositional objects. Notably, SB-GFlowNet approximates the initial posterior using a standard GFlowNet and subsequently updates it using a tailored procedure that requires only the newly observed data. Our case studies in linear preference learning and phylogenetic inference showcase the effectiveness of SB-GFlowNets in sampling from an unnormalized posterior in a streaming setting. As expected, we also observe that SB-GFlowNets is significantly faster than repeatedly training a GFlowNet from scratch to sample from the full posterior.

Mixtures of Experts (MoE) are Machine Learning models that involve partitioning the input space, with a separate "expert" model trained on each partition. Recently, MoE have become popular as components in today's large language models as a means to reduce training and inference costs. There, the partitioning function and the experts are both learnt jointly via gradient descent on the log-likelihood. In this paper we focus on studying the efficiency of the Expectation Maximization (EM) algorithm for the training of MoE models. We first rigorously analyze EM for the cases of linear or logistic experts, where we show that EM is equivalent to Mirror Descent with unit step size and a Kullback-Leibler Divergence regularizer. This perspective allows us to derive new convergence results and identify conditions for local linear convergence based on the signal-to-noise ratio (SNR). Experiments on synthetic and (small-scale) real-world data show that EM outperforms the gradient descent algorithm both in terms of convergence rate and the achieved accuracy.

Many important phenomena in scientific fields such as climate, neuroscience, and epidemiology are naturally represented as spatiotemporal gridded data with complex interactions. For example, in climate science, researchers aim to uncover how large-scale events, such as the North Atlantic Oscillation (NAO) and the Antarctic Oscillation (AAO), influence other global processes. Inferring causal relationships from these data is a challenging problem compounded by the high dimensionality of such data and the correlations between spatially proximate points. We present SPACY (SPAtiotemporal Causal discoverY), a novel framework based on variational inference, designed to explicitly model latent time-series and their causal relationships from spatially confined modes in the data. Our method uses an end-to-end training process that maximizes an evidence-lower bound (ELBO) for the data likelihood. Theoretically, we show that, under some conditions, the latent variables are identifiable up to transformation by an invertible matrix. Empirically, we show that SPACY outperforms state-of-the-art baselines on synthetic data, remains scalable for large grids, and identifies key known phenomena from real-world climate data.

Missing data is a common problem in finance and often requires methods to fill in the gaps, or in other words, imputation. In this work, we focused on the imputation of missing implied volatilities for FX options. Prior work has used variational autoencoders (VAEs), a neural network-based approach, to solve this problem; however, using stronger classical baselines such as Heston with jumps can significantly outperform their results. We show that simple modifications to the architecture of the VAE lead to significant imputation performance improvements (e.g., in low missingness regimes, nearly cutting the error by half), removing the necessity of using $\beta$-VAEs. Further, we modify the VAE imputation algorithm in order to better handle the uncertainty in data, as well as to obtain accurate uncertainty estimates around imputed values.

A large amount of information in today's world is now stored in knowledge bases. Named Entity Recognition (NER) is a process of extracting, disambiguation, and linking an entity from raw text to insightful and structured knowledge bases. More concretely, it is identifying and classifying entities in the text that are crucial for Information Extraction, Semantic Annotation, Question Answering, Ontology Population, and so on. The process of NER has evolved in the last three decades since it first appeared in 1996. In this survey, we study the evolution of techniques employed for NER and compare the results, starting from supervised to the developing unsupervised learning methods.