Bird's eye view (BEV) is widely adopted by most of the current point cloud detectors due to the applicability of well-explored 2D detection techniques. However, existing methods obtain BEV features by simply collapsing voxel or point features along the height dimension, which causes the heavy loss of 3D spatial information. To alleviate the information loss, we propose a novel point cloud detection network based on a Multi-level feature dimensionality reduction strategy, called MDRNet. In MDRNet, the Spatial-aware Dimensionality Reduction (SDR) is designed to dynamically focus on the valuable parts of the object during voxel-to-BEV feature transformation. Furthermore, the Multi-level Spatial Residuals (MSR) is proposed to fuse the multi-level spatial information in the BEV feature maps. Extensive experiments on nuScenes show that the proposed method outperforms the state-of-the-art methods. The code will be available upon publication.

In medical genetics, each genetic variant is evaluated as an independent entity regarding its clinical importance. However, in most complex diseases, variant combinations in specific gene networks, rather than the presence of a particular single variant, predominates. In the case of complex diseases, disease status can be evaluated by considering the success level of a team of specific variants. We propose a high dimensional modelling based method to analyse all the variants in a gene network together. To evaluate our method, we selected two gene networks, mTOR and TGF-Beta. For each pathway, we generated 400 control and 400 patient group samples. mTOR and TGF-? pathways contain 31 and 93 genes of varying sizes, respectively. We produced Chaos Game Representation images for each gene sequence to obtain 2-D binary patterns. These patterns were arranged in succession, and a 3-D tensor structure was achieved for each gene network. Features for each data sample were acquired by exploiting Enhanced Multivariance Products Representation to 3-D data. Features were split as training and testing vectors. Training vectors were employed to train a Support Vector Machines classification model. We achieved more than 96% and 99% classification accuracies for mTOR and TGF-Beta networks, respectively, using a limited amount of training samples.

Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with non-asymptotic gradient norm guarantees. Our convergence analysis is based on a gradient Lipschitz condition with respect to a Mahalanobis norm, inspired by a recent progress on cyclic block coordinate methods. In deterministic settings, our convergence guarantee matches the guarantee of (full-gradient) gradient descent, but with the gradient Lipschitz constant being defined w.r.t.~a Mahalanobis norm. In stochastic settings, we use recursive variance reduction to decrease the per-iteration cost and match the arithmetic operation complexity of current optimal stochastic full-gradient methods, with a unified analysis for both finite-sum and infinite-sum cases. We prove a faster linear convergence result when a Polyak-{\L}ojasiewicz (P{\L}) condition holds. To our knowledge, this work is the first to provide non-asymptotic convergence guarantees -- variance-reduced or not -- for a cyclic block coordinate method in general composite (smooth + nonsmooth) nonconvex settings. Our experimental results demonstrate the efficacy of the proposed cyclic scheme in training deep neural nets.

Human visual perception can easily generalize to out-of-distributed visual data, which is far beyond the capability of modern machine learning models. Domain generalization (DG) aims to close this gap, with existing DG methods mainly focusing on the loss function design. In this paper, we propose to explore an orthogonal direction, i.e., the design of the backbone architecture. It is motivated by an empirical finding that transformer-based models trained with empirical risk minimization (ERM) outperform CNN-based models employing state-of-the-art (SOTA) DG algorithms on multiple DG datasets. We develop a formal framework to characterize a network's robustness to distribution shifts by studying its architecture's alignment with the correlations in the dataset. This analysis guides us to propose a novel DG model built upon vision transformers, namely Generalizable Mixture-of-Experts (GMoE). Extensive experiments on DomainBed demonstrate that GMoE trained with ERM outperforms SOTA DG baselines by a large margin. Moreover, GMoE is complementary to existing DG methods and its performance is substantially improved when trained with DG algorithms.

This article belongs to the series "Probabilistic Deep Learning". This weekly series covers probabilistic approaches to deep learning. The main goal is to extend deep learning models to quantify uncertainty, i.e., know what they do not know. In this article, we will introduce the concept of probabilistic logistic regression, a powerful technique that allows for the inclusion of uncertainty in the prediction process. We will explore how this approach can lead to more robust and accurate predictions, especially in cases where the data is noisy, or the model is overfitting.

Signature-based techniques give mathematical insight into the interactions between complex streams of evolving data. These insights can be quite naturally translated into numerical approaches to understanding streamed data, and perhaps because of their mathematical precision, have proved useful in analysing streamed data in situations where the data is irregular, and not stationary, and the dimension of the data and the sample sizes are both moderate. Understanding streamed multi-modal data is exponential: a word in $n$ letters from an alphabet of size $d$ can be any one of $d^n$ messages. Signatures remove the exponential amount of noise that arises from sampling irregularity, but an exponential amount of information still remain. This survey aims to stay in the domain where that exponential scaling can be managed directly. Scalability issues are an important challenge in many problems but would require another survey article and further ideas. This survey describes a range of contexts where the data sets are small enough to remove the possibility of massive machine learning, and the existence of small sets of context free and principled features can be used effectively. The mathematical nature of the tools can make their use intimidating to non-mathematicians. The examples presented in this article are intended to bridge this communication gap and provide tractable working examples drawn from the machine learning context. Notebooks are available online for several of these examples. This survey builds on the earlier paper of Ilya Chevryev and Andrey Kormilitzin which had broadly similar aims at an earlier point in the development of this machinery. This article illustrates how the theoretical insights offered by signatures are simply realised in the analysis of application data in a way that is largely agnostic to the data type.

We present a model inversion algorithm, CKLEMAP, for data assimilation and parameter estimation in partial differential equation models of physical systems with spatially heterogeneous parameter fields. These fields are approximated using low-dimensional conditional Karhunen-Lo\'{e}ve expansions, which are constructed using Gaussian process regression models of these fields trained on the parameters' measurements. We then assimilate measurements of the state of the system and compute the maximum a posteriori estimate of the CKLE coefficients by solving a nonlinear least-squares problem. When solving this optimization problem, we efficiently compute the Jacobian of the vector objective by exploiting the sparsity structure of the linear system of equations associated with the forward solution of the physics problem. The CKLEMAP method provides better scalability compared to the standard MAP method. In the MAP method, the number of unknowns to be estimated is equal to the number of elements in the numerical forward model. On the other hand, in CKLEMAP, the number of unknowns (CKLE coefficients) is controlled by the smoothness of the parameter field and the number of measurements, and is in general much smaller than the number of discretization nodes, which leads to a significant reduction of computational cost with respect to the standard MAP method. To show its advantage in scalability, we apply CKLEMAP to estimate the transmissivity field in a two-dimensional steady-state subsurface flow model of the Hanford Site by assimilating synthetic measurements of transmissivity and hydraulic head. We find that the execution time of CKLEMAP scales nearly linearly as $N^{1.33}$, where $N$ is the number of discretization nodes, while the execution time of standard MAP scales as $N^{2.91}$. The CKLEMAP method improved execution time without sacrificing accuracy when compared to the standard MAP.

Although Artificial Neural Networks (ANNs) are very accurate predicting tools if compared to more conventional survival models (Topol, 2019; Zeng et al., 2022; Ivanov et al., 2022), they are often seen as black boxes. ANN models are indeed very difficult to interpret and it is challenging to identify which predictors are the most relevant (May et al., 2011). In contrast, semi-parametric hazard based survival models (Andersen et al. (1993)) are examples of interpretable models, whose hazards can measure (directly or indirectly) the effect of each covariate on the outcome of interest. In order to properly model the temporal evolution of the survival process, including longitudinal information (e.g., biomarkers, health status, clinical measurements) as time-dependent covariates is often informative. These covariates are usually internal and they require extra modeling to predict survival functions accurately (Cortese and Andersen, 2010).

The most effective dimensionality reduction procedures produce interpretable features from the raw input space while also providing good performance for downstream supervised learning tasks. For many methods, this requires optimizing one or more hyperparameters for a specific task, which can limit generalizability. In this study we propose sparse compressed agglomeration (SparCA), a novel dimensionality reduction procedure that involves a multistep hierarchical feature grouping, compression, and feature selection process. We demonstrate the characteristics and performance of the SparCA method across heterogenous synthetic and real-world datasets, including images, natural language, and single cell gene expression data. Our results show that SparCA is applicable to a wide range of data types, produces highly interpretable features, and shows compelling performance on downstream supervised learning tasks without the need for hyperparameter tuning.

The interest in Artificial Intelligence (AI) and its applications has seen unprecedented growth in the last few years. The success can be partly attributed to the advancements of deep neural networks made in the sub-fields of AI such as Computer Vision (CV) and Natural Language Processing (NLP). The promising research area that this dissertation focuses on is visual and language understanding which involves many challenging tasks, i.e., classification, detection, segmentation, machine translation and captioning, etc. The state-of-the-art methods for solving these problems usually involves only two parts: source data and target labels, which is rather insufficient especially when the dataset is small. Meanwhile, many external tools or sources can provide extra useful information (external knowledge) that can help improve the performance of these methods. For example, a detection model has been applied to provide better object features than state-of-the-art ResNet for image captioning models. Inspired by this observation, we developed a methodology that we can first extract external knowledge and then integrate it with the original models. The external knowledge has to be extracted from the dataset, or can directly come from external, e.g., grammar rules or scene graphs. We apply this methodology to different AI tasks, including machine translation and image captioning and improve the original state-of-the-art models by a large margin.