Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved

Optimisation Methods For Training Deep Neural Networks in Speech Recognition

Automatic Speech Recognition (ASR) is an example of a sequence to sequence level classification task where, given an acoustic waveform, the goal is to produce the correct word level hypotheses. In machine learning, a classification problem such as ASR is solved in two stages: an inference stage that models the uncertainty associated with the choice of hypothesis given the acoustic waveform using a mathematical model, and a decision stage which employs the inference model in conjunction with decision theory to make optimal class assignments. With the advent of careful network initialisation and GPU computing, hybrid Hidden Markov Models (HMMs) augmented with Deep Neural Networks (DNNs) have shown to outperform traditional HMMs using Gaussian Mixture Models (GMMs) in solving the inference problem for ASR. In comparison to GMMs, DNNs possess a better capability to model the underlying non-linear data manifold due to their deep and complex structure. While the structure of such models gives rich modelling capability, it also creates complex dependencies between the parameters which can make learning difficult via first order stochastic gradient descent (SGD). The task of finding the best procedure to train DNNs continues to be an active area of research and has been made even more challenging by the availability of ever more training data. This thesis focuses on designing better optimisation approaches to train hybrid HMM-DNN models using sequence level discriminative criterion which is a natural loss function that preserves the sequential ordering of frames within a spoken utterance. The thesis presents an implementation of the second order Hessian Free (HF) optimisation method, and shows how the method can made efficient through appropriate modifications to the Conjugate Gradient algorithm. To achieve better convergence than SGD, this work explores the Natural Gradient method to train DNNs with discriminative sequence training. In the DNN literature, the method has been applied to train models for the Maximum Likelihood objective criterion. A novel contribution of this thesis is to extend this approach to the domain of Minimum Bayes Risk objective functions for discriminative sequence training. With sigmoid models trained on a 50hr and 200hr training set from the Multi-Genre Broadcast 1 (MGB1) transcription task, the NG method applied in a HF styled optimisation framework is shown to achieve better Word Error Rate (WER) reductions on the MGB1 development set than SGD from sequence training. This thesis also addresses the particular issue of overfitting between the training criterion and WER, that primarily arises during sequence training of DNN models that use Rectified Linear Units (ReLUs) as activation functions. It is shown how by scaling with the Gauss Newton matrix, the HF method unlike other approaches can overcome this issue. Seeing that different optimisers work best with different models, it is attractive to have a consistent optimisation framework that is agnostic to the choice of activation function. To address the issue, this thesis develops the geometry of the underlying function space captured by different realisations of DNN model parameters, and presents the design considerations for an optimisation algorithm to be well defined on this space. Building on this analysis, a novel optimisation technique called NGHF is presented that uses both the direction of steepest descent on a probabilistic manifold and local curvature information to effectively probe the error surface. The basis of the method relies on an alternative derivation of Taylor’s theorem using the concepts of manifolds, tangent vectors and directional derivatives from the perspective of Information Geometry. Apart from being well defined on the function space, when framed within a HF style optimisation framework, the method of NGHF is shown to achieve the greatest WER reductions from sequence training on the MGB1 development set with both sigmoid and ReLU based models trained on the 200hr MGB1 training set. The evaluation of the above optimisation methods in training different DNN model architectures is also presented.IDB Cambridge International Scholarshi

Topological data analysis of organoids

Organoids are multi-cellular structures which are cultured in vitro from stem cells to resemble specific organs (e.g., colon, liver) in their three- dimensional composition. The gene expression and the tissue composition of organoids constantly affect each other. Dynamic changes in the shape, cellular composition and transcriptomic profile of these model systems can be used to understand the effect of mutations and treatments in health and disease. In this thesis, I propose new techniques in the field of topological data analysis (TDA) to analyse the gene expression and the morphology of organoids. I use TDA methods, which are inspired by topology, to analyse and quantify the continuous structure of single-cell RNA sequencing data, which is embedded in high dimensional space, and the shape of an organoid. For single-cell RNA sequencing data, I developed the multiscale Laplacian score (MLS) and the UMAP diffusion cover, which both extend and im- prove existing topological analysis methods. I demonstrate the utility of these techniques by applying them to a published benchmark single-cell data set and a data set of mouse colon organoids. The methods validate previously identified genes and detect additional genes with known involvement cancers. To study the morphology of organoids I propose DETECT, a rotationally invariant signature of dynamically changing shapes. I demonstrate the efficacy of this method on a data set of segmented videos of mouse small intestine organoid experiments and show that it outperforms classical shape descriptors. I verify the method on a synthetic organoid data set and illustrate how it generalises to 3D to conclude that DETECT offers rigorous quantification of organoids and opens up computationally scalable methods for distinguishing different growth regimes and assessing treatment effects. Finally, I make a theoretical contribution to the statistical inference of the method underlying DETECT

Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimization

Recent research indicates that the performance of machine learning models can be improved by aligning the geometry of the latent space with the underlying data structure. Rather than relying solely on Euclidean space, researchers have proposed using hyperbolic and spherical spaces with constant curvature, or combinations thereof, to better model the latent space and enhance model performance. However, little attention has been given to the problem of automatically identifying the optimal latent geometry for the downstream task. We mathematically define this novel formulation and coin it as neural latent geometry search (NLGS). More specifically, we introduce a principled method that searches for a latent geometry composed of a product of constant curvature model spaces with minimal query evaluations. To accomplish this, we propose a novel notion of distance between candidate latent geometries based on the Gromov-Hausdorff distance from metric geometry. In order to compute the Gromov-Hausdorff distance, we introduce a mapping function that enables the comparison of different manifolds by embedding them in a common high-dimensional ambient space. Finally, we design a graph search space based on the calculated distances between candidate manifolds and use Bayesian optimization to search for the optimal latent geometry in a query-efficient manner. This is a general method which can be applied to search for the optimal latent geometry for a variety of models and downstream tasks. Extensive experiments on synthetic and real-world datasets confirm the efficacy of our method in identifying the optimal latent geometry for multiple machine learning problems