In this paper, we propose a Generalized Unsupervised Manifold Alignment (GU-MA) method to build the connections between different but correlated datasets without any known correspondences. Based on the assumption that datasets of the same theme usually have similar manifold structures, GUMA is formulated into an explicit integer optimization problem considering the structure matching and preserving criteria, as well as the feature comparability of the corresponding points in the mutual embedding space. The main benefits of this model include: (1) simultaneous discovery and alignment of manifold structures; (2) fully unsupervised matching without any pre-specified correspondences; (3) efficient iterative alignment without computations in all permutation cases. Experimental results on dataset matching and real-world applications demonstrate the effectiveness and the practicability of our manifold alignment method.

In urban environments for delivery robots, particularly in areas such as campuses and towns, many custom features defy standard road semantic categorizations. Addressing this challenge, our paper introduces a method leveraging Salient Object Detection (SOD) to extract these unique features, employing them as pivotal factors for enhanced robot loop closure and localization. Traditional geometric feature-based localization is hampered by fluctuating illumination and appearance changes. Our preference for SOD over semantic segmentation sidesteps the intricacies of classifying a myriad of non-standardized urban features. To achieve consistent ground features, the Motion Compensate IPM (MC-IPM) technique is implemented, capitalizing on motion for distortion compensation and subsequently selecting the most pertinent salient ground features through moment computations. For thorough evaluation, we validated the saliency detection and localization performances to the real urban scenarios. Project page: https://sites.google.com/view/salient-ground-feature/home.

In this paper, we propose a Generalized Unsupervised Manifold Alignment (GU-MA) method to build the connections between different but correlated datasets without any known correspondences. Based on the assumption that datasets of the same theme usually have similar manifold structures, GUMA is formulated into an explicit integer optimization problem considering the structure matching and preserving criteria, as well as the feature comparability of the corresponding points in the mutual embedding space. The main benefits of this model include: (1) simultaneous discovery and alignment of manifold structures; (2) fully unsupervised matching without any pre-specified correspondences; (3) efficient iterative alignment without computations in all permutation cases. Experimental results on dataset matching and real-world applications demonstrate the effectiveness and the practicability of our manifold alignment method.

In supervised learning of neural networks and regression models, understanding the dynamics of optimization algorithms, and in particular stochastic gradient descent (SGD), is of utmost importance. However, despite much progress in a number of directions, this still remains a highly challenging theoretical problem. A fruitful approach that allows making analytical progress consists of suitably approximating SGD by a continuous time approximation, henceforth called stochastic gradient flow (SGF). In this contribution, we build up on this approach, to develop a general formalism characterizing the dynamics of the stochastic process, and apply it to the investigation of the test risk (or generalization error) as a function of time. As is well known, the classical bias-variance trade-off has been challenged in a number of models displaying the double descent phenomenon [1, 2, 3]. Analytical derivations of double descent curves have been achieved for relatively simple models, but are limited to the use of least squares estimators (no dynamics) and pure gradient flow (GF) approximations of gradient descent (GD). The present work goes one step further by investigating the effects of stochasticity on the double descent curve. Our main contributions are summarized as follows: C1 We consider a general Itô stochastic differential equation (SDE) and represent the Markovian transition probability as a path integral, Eq. (12). A general'explicit' formula for the transition probability, Eq. (18), is derived in the limit of a small learning rate by using a Laplace approximation.

We study the implicit regularization of mini-batch stochastic gradient descent, when applied to the fundamental problem of least squares regression. We leverage a continuous-time stochastic differential equation having the same moments as stochastic gradient descent, which we call stochastic gradient flow. We give a bound on the excess risk of stochastic gradient flow at time $t$, over ridge regression with tuning parameter $\lambda = 1/t$. The bound may be computed from explicit constants (e.g., the mini-batch size, step size, number of iterations), revealing precisely how these quantities drive the excess risk. Numerical examples show the bound can be small, indicating a tight relationship between the two estimators. We give a similar result relating the coefficients of stochastic gradient flow and ridge. These results hold under no conditions on the data matrix $X$, and across the entire optimization path (not just at convergence).

Hierarchical planners that produce interpretable and appropriate plans are desired, especially in its application to supporting human decision making. In the typical development of the hierarchical planners, higher-level planners and symbol grounding functions are manually created, and this manual creation requires much human effort. In this paper, we propose a framework that can automatically refine symbol grounding functions and a high-level planner to reduce human effort for designing these modules. In our framework, symbol grounding and high-level planning, which are based on manually-designed knowledge bases, are modeled with semi-Markov decision processes. A policy gradient method is then applied to refine the modules, in which two terms for updating the modules are considered. The first term, called a reinforcement term, contributes to updating the modules to improve the overall performance of a hierarchical planner to produce appropriate plans. The second term, called a penalty term, contributes to keeping refined modules consistent with the manually-designed original modules. Namely, it keeps the planner, which uses the refined modules, producing interpretable plans. We perform preliminary experiments to solve the Mountain car problem, and its results show that a manually-designed high-level planner and symbol grounding function were successfully refined by our framework.

In this paper, we propose a Generalized Unsupervised Manifold Alignment (GU-MA) method to build the connections between different but correlated datasets without any known correspondences. Based on the assumption that datasets of the same theme usually have similar manifold structures, GUMA is formulated into an explicit integer optimization problem considering the structure matching and preserving criteria, as well as the feature comparability of the corresponding points in the mutual embedding space. The main benefits of this model include: (1) simultaneous discovery and alignment of manifold structures; (2) fully unsupervised matchingwithout any pre-specified correspondences; (3) efficient iterative alignment without computations in all permutation cases. Experimental results on dataset matching and real-world applications demonstrate the effectiveness and the practicability of our manifold alignment method.

In this paper we address the following question: "Can we approximately sample from a Bayesian posterior distribution if we are only allowed to touch a small mini-batch of data-items for every sample we generate?". An algorithm based on the Langevin equation with stochastic gradients (SGLD) was previously proposed to solve this, but its mixing rate was slow. By leveraging the Bayesian Central Limit Theorem, we extend the SGLD algorithm so that at high mixing rates it will sample from a normal approximation of the posterior, while for slow mixing rates it will mimic the behavior of SGLD with a pre-conditioner matrix. As a bonus, the proposed algorithm is reminiscent of Fisher scoring (with stochastic gradients) and as such an efficient optimizer during burn-in.