Autonomous underwater vehicles (AUVs) are becoming standard tools for underwater exploration and seabed mapping in both scientific and industrial applications \cite{graham2022rapid, stenius2022system}. Their capacity to dive untethered allows them to reach areas inaccessible to surface vessels and to collect data more closely to the seafloor, regardless of the water depth. However, their navigation autonomy remains bounded by the accuracy of their dead reckoning (DR) estimate of their global position, severely limited in the absence of a priori maps of the area and GPS signal. Global localization systems equivalent to the later exists for the underwater domain, such as LBL or USBL. However they involve expensive external infrastructure and their reliability decreases with the distance to the AUV, making them unsuitable for deep sea surveys.

We propose a new framework for differentially private optimization of convex functions which are Lipschitz in an arbitrary norm $\|\cdot\|$. Our algorithms are based on a regularized exponential mechanism which samples from the density $\propto \exp(-k(F+\mu r))$ where $F$ is the empirical loss and $r$ is a regularizer which is strongly convex with respect to $\|\cdot\|$, generalizing a recent work of [Gopi, Lee, Liu '22] to non-Euclidean settings. We show that this mechanism satisfies Gaussian differential privacy and solves both DP-ERM (empirical risk minimization) and DP-SCO (stochastic convex optimization) by using localization tools from convex geometry. Our framework is the first to apply to private convex optimization in general normed spaces and directly recovers non-private SCO rates achieved by mirror descent as the privacy parameter $\epsilon \to \infty$. As applications, for Lipschitz optimization in $\ell_p$ norms for all $p \in (1, 2)$, we obtain the first optimal privacy-utility tradeoffs; for $p = 1$, we improve tradeoffs obtained by the recent works [Asi, Feldman, Koren, Talwar '21, Bassily, Guzman, Nandi '21] by at least a logarithmic factor. Our $\ell_p$ norm and Schatten-$p$ norm optimization frameworks are complemented with polynomial-time samplers whose query complexity we explicitly bound.

Learning classifiers using skewed or imbalanced datasets can occasionally lead to classification issues; this is a serious issue. In some cases, one class contains the majority of examples while the other, which is frequently the more important class, is nevertheless represented by a smaller proportion of examples. Using this kind of data could make many carefully designed machine-learning systems ineffective. High training fidelity was a term used to describe biases vs. all other instances of the class. The best approach to all possible remedies to this issue is typically to gain from the minority class. The article examines the most widely used methods for addressing the problem of learning with a class imbalance, including data-level, algorithm-level, hybrid, cost-sensitive learning, and deep learning, etc. including their advantages and limitations. The efficiency and performance of the classifier are assessed using a myriad of evaluation metrics.

A key goal of unsupervised learning is to go beyond density estimation and sample generation to reveal the structure inherent within observed data. Such structure can be expressed in the pattern of interactions between explanatory latent variables captured through a probabilistic graphical model. Although the learning of structured graphical models has a long history, much recent work in unsupervised modelling has instead emphasised flexible deep-network-based generation, either transforming independent latent generators to model complex data or assuming that distinct observed variables are derived from different latent nodes. Here, we extend amortised variational inference to incorporate structured factors over multiple variables, able to capture the observation-induced posterior dependence between latents that results from ``explaining away'' and thus allow complex observations to depend on multiple nodes of a structured graph. We show that appropriately parametrised factors can be combined efficiently with variational message passing in rich graphical structures. We instantiate the framework in nonlinear Gaussian Process Factor Analysis, evaluating the structured recognition framework using synthetic data from known generative processes. We fit the GPFA model to high-dimensional neural spike data from the hippocampus of freely moving rodents, where the model successfully identifies latent signals that correlate with behavioural covariates.

Large pretrained Transformer-based language models like BERT and GPT have changed the landscape of Natural Language Processing (NLP). However, fine tuning such models still requires a large number of training examples for each target task, thus annotating multiple datasets and training these models on various downstream tasks becomes time consuming and expensive. In this work, we propose a simple extension of the Prototypical Networks for few-shot text classification. Our main idea is to replace the class prototypes by Gaussians and introduce a regularization term that encourages the examples to be clustered near the appropriate class centroids. Experimental results show that our method outperforms various strong baselines on 13 public and 4 internal datasets. Furthermore, we use the class distributions as a tool for detecting potential out-of-distribution (OOD) data points during deployment.

Pre-trained Transformers currently dominate most NLP tasks. They impose, however, limits on the maximum input length (512 sub-words in BERT), which are too restrictive in the legal domain. Even sparse-attention models, such as Longformer and BigBird, which increase the maximum input length to 4,096 sub-words, severely truncate texts in three of the six datasets of LexGLUE. Simpler linear classifiers with TF-IDF features can handle texts of any length, require far less resources to train and deploy, but are usually outperformed by pre-trained Transformers. We explore two directions to cope with long legal texts: (i) modifying a Longformer warm-started from LegalBERT to handle even longer texts (up to 8,192 sub-words), and (ii) modifying LegalBERT to use TF-IDF representations. The first approach is the best in terms of performance, surpassing a hierarchical version of LegalBERT, which was the previous state of the art in LexGLUE. The second approach leads to computationally more efficient models at the expense of lower performance, but the resulting models still outperform overall a linear SVM with TF-IDF features in long legal document classification.

In order to deal with variant-length long videos, prior works extract multi-modal features and fuse them to predict students' engagement intensity. In this paper, we present a new end-to-end method Class Attention in Video Transformer (CavT), which involves a single vector to process class embedding and to uniformly perform end-to-end learning on variant-length long videos and fixed-length short videos. Furthermore, to address the lack of sufficient samples, we propose a binary-order representatives sampling method (BorS) to add multiple video sequences of each video to augment the training set. BorS+CavT not only achieves the state-of-the-art MSE (0.0495) on the EmotiW-EP dataset, but also obtains the state-of-the-art MSE (0.0377) on the DAiSEE dataset. The code and models have been made publicly available at https://github.com/mountainai/cavt.

Simulation-based inference (SBI) solves statistical inverse problems by repeatedly running a stochastic simulator and inferring posterior distributions from model-simulations. To improve simulation efficiency, several inference methods take a sequential approach and iteratively adapt the proposal distributions from which model simulations are generated. However, many of these sequential methods are difficult to use in practice, both because the resulting optimisation problems can be challenging and efficient diagnostic tools are lacking. To overcome these issues, we present Truncated Sequential Neural Posterior Estimation (TSNPE). TSNPE performs sequential inference with truncated proposals, sidestepping the optimisation issues of alternative approaches. In addition, TSNPE allows to efficiently perform coverage tests that can scale to complex models with many parameters. We demonstrate that TSNPE performs on par with previous methods on established benchmark tasks. We then apply TSNPE to two challenging problems from neuroscience and show that TSNPE can successfully obtain the posterior distributions, whereas previous methods fail. Overall, our results demonstrate that TSNPE is an efficient, accurate, and robust inference method that can scale to challenging scientific models.

Machine learning and deep learning classification models are data-driven, and the model and the data jointly determine their classification performance. It is biased to evaluate the model's performance only based on the classifier accuracy while ignoring the data separability. Sometimes, the model exhibits excellent accuracy, which might be attributed to its testing on highly separable data. Most of the current studies on data separability measures are defined based on the distance between sample points, but this has been demonstrated to fail in several circumstances. In this paper, we propose a new separability measure--the rate of separability (RS), which is based on the data coding rate. We validate its effectiveness as a supplement to the separability measure by comparing it to four other distance-based measures on synthetic datasets. Then, we demonstrate the positive correlation between the proposed measure and recognition accuracy in a multi-task scenario constructed from a real dataset. Finally, we discuss the methods for evaluating the classification performance of machine learning and deep learning models considering data separability.

We harness a least squares formulation and mobilize the stochastic gradient descent framework. Therefore, we obtain a randomized classifier with performance that is very comparable to that of full data LDA while requiring access to only one row of the training data at a time. We present convergence guarantees for the sketched predictions on new data within a fixed number of iterations. These guarantees account for both the Gaussian modeling assumptions on the data and algorithmic randomness from the sketching procedure. Finally, we demonstrate performance with varying step-sizes and numbers of iterations. Our numerical experiments demonstrate that sketched LDA can offer a very viable alternative to full data LDA when the data may be too large for full data analysis.