When a patient is admitted to the intensive care unit (ICU) after a traumatic brain injury (TBI), an early prognosis is essential for baseline risk adjustment and shared decision making. TBI outcomes are commonly categorised by the Glasgow Outcome Scale-Extended (GOSE) into 8, ordered levels of functional recovery at 6 months after injury. Existing ICU prognostic models predict binary outcomes at a certain threshold of GOSE (e.g., prediction of survival [GOSE>1] or functional independence [GOSE>4]). We aimed to develop ordinal prediction models that concurrently predict probabilities of each GOSE score. From a prospective cohort (n=1,550, 65 centres) in the ICU stratum of the Collaborative European NeuroTrauma Effectiveness Research in TBI (CENTER-TBI) patient dataset, we extracted all clinical information within 24 hours of ICU admission (1,151 predictors) and 6-month GOSE scores. We analysed the effect of 2 design elements on ordinal model performance: (1) the baseline predictor set, ranging from a concise set of 10 validated predictors to a token-embedded representation of all possible predictors, and (2) the modelling strategy, from ordinal logistic regression to multinomial deep learning. With repeated k-fold cross-validation, we found that expanding the baseline predictor set significantly improved ordinal prediction performance while increasing analytical complexity did not. Half of these gains could be achieved with the addition of 8 high-impact predictors (2 demographic variables, 4 protein biomarkers, and 2 severity assessments) to the concise set. At best, ordinal models achieved 0.76 (95% CI: 0.74-0.77) ordinal discrimination ability (ordinal c-index) and 57% (95% CI: 54%-60%) explanation of ordinal variation in 6-month GOSE (Somers' D). Our results motivate the search for informative predictors for higher GOSE and the development of ordinal dynamic prediction models.

Wearable and IoT devices requiring positioning and localisation services grow in number exponentially every year. This rapid growth also produces millions of data entries that need to be pre-processed prior to being used in any indoor positioning system to ensure the data quality and provide a high Quality of Service (QoS) to the end-user. In this paper, we offer a novel and straightforward data cleansing algorithm for WLAN fingerprinting radio maps. This algorithm is based on the correlation among fingerprints using the Received Signal Strength (RSS) values and the Access Points (APs)'s identifier. We use those to compute the correlation among all samples in the dataset and remove fingerprints with low level of correlation from the dataset. We evaluated the proposed method on 14 independent publicly-available datasets. As a result, an average of 14% of fingerprints were removed from the datasets. The 2D positioning error was reduced by 2.7% and 3D positioning error by 5.3% with a slight increase in the floor hit rate by 1.2% on average. Consequently, the average speed of position prediction was also increased by 14%.

We study the first gradient descent step on the first-layer parameters $\boldsymbol{W}$ in a two-layer neural network: $f(\boldsymbol{x}) = \frac{1}{\sqrt{N}}\boldsymbol{a}^\top\sigma(\boldsymbol{W}^\top\boldsymbol{x})$, where $\boldsymbol{W}\in\mathbb{R}^{d\times N}, \boldsymbol{a}\in\mathbb{R}^{N}$ are randomly initialized, and the training objective is the empirical MSE loss: $\frac{1}{n}\sum_{i=1}^n (f(\boldsymbol{x}_i)-y_i)^2$. In the proportional asymptotic limit where $n,d,N\to\infty$ at the same rate, and an idealized student-teacher setting, we show that the first gradient update contains a rank-1 "spike", which results in an alignment between the first-layer weights and the linear component of the teacher model $f^*$. To characterize the impact of this alignment, we compute the prediction risk of ridge regression on the conjugate kernel after one gradient step on $\boldsymbol{W}$ with learning rate $\eta$, when $f^*$ is a single-index model. We consider two scalings of the first step learning rate $\eta$. For small $\eta$, we establish a Gaussian equivalence property for the trained feature map, and prove that the learned kernel improves upon the initial random features model, but cannot defeat the best linear model on the input. Whereas for sufficiently large $\eta$, we prove that for certain $f^*$, the same ridge estimator on trained features can go beyond this "linear regime" and outperform a wide range of random features and rotationally invariant kernels. Our results demonstrate that even one gradient step can lead to a considerable advantage over random features, and highlight the role of learning rate scaling in the initial phase of training.

The Partial Least Square Regression (PLSR) exhibits admirable competence for predicting continuous variables from inter-correlated brain recordings in the brain-computer interface. However, PLSR is in essence formulated based on the least square criterion, thus, being non-robust with respect to noises. The aim of this study is to propose a new robust implementation for PLSR. To this end, the maximum correntropy criterion (MCC) is used to propose a new robust variant of PLSR, called as Partial Maximum Correntropy Regression (PMCR). The half-quadratic optimization is utilized to calculate the robust projectors for the dimensionality reduction, and the regression coefficients are optimized by a fixed-point approach. We evaluate the proposed PMCR with a synthetic example and the public Neurotycho electrocorticography (ECoG) datasets. The extensive experimental results demonstrate that, the proposed PMCR can achieve better prediction performance than the conventional PLSR and existing variants with three different performance indicators in high-dimensional and noisy regression tasks. PMCR can suppress the performance degradation caused by the adverse noise, ameliorating the decoding robustness of the brain-computer interface.

Natural processes may undergo transient periods of nonstationarity which produce lasting change in process behavior across time. When driven by exogeneous influences these changes can be challenging to predict in advance. To circumvent this challenge, works in online (sequential) change detection aim to deduce the occurrence of change in process behavior as it occurs via direct observation of an online data stream. While such changes in process behavior are most commonly modeled via change-points, in which the parameters and/or densities defining an associated process model are assumed to undergo an abrupt and instantaneous transition, changes in the behavior of some processes may occur gradually, taking time to reach their full effect. In such cases change-point models may be ill suited, producing either inaccurate estimates for the timing of these changes or, when this gradual change occurs slowly and when change detection is performed concurrently with model estimation, failing to properly detect change occurrence, as we show empirically in Section 4. This effect can have a significant impact in application, where automated system controls may not be appropriately applied at the correct times, and can result in inaccurate models of process behavior during and after this gradual change.

In many applications, data can be heterogeneous in the sense of spanning latent groups with different underlying distributions. When predictive models are applied to such data the heterogeneity can affect both predictive performance and interpretability. Building on developments at the intersection of unsupervised learning and regularised regression, we propose an approach for heterogeneous data that allows joint learning of (i) explicit multivariate feature distributions, (ii) high-dimensional regression models and (iii) latent group labels, with both (i) and (ii) specific to latent groups and both elements informing (iii). The approach is demonstrably effective in high dimensions, combining data reduction for computational efficiency with a re-weighting scheme that retains key signals even when the number of features is large. We discuss in detail these aspects and their impact on modelling and computation, including EM convergence. The approach is modular and allows incorporation of data reductions and high-dimensional estimators that are suitable for specific applications. We show results from extensive simulations and real data experiments, including highly non-Gaussian data. Our results allow efficient, effective analysis of high-dimensional data in settings, such as biomedicine, where both interpretable prediction and explicit feature space models are needed but hidden heterogeneity may be a concern.

We propose a unified view on two widely used data visualization techniques: Self-Organizing Maps (SOMs) and Stochastic Neighbor Embedding (SNE). We show that they can both be derived from a common mathematical framework. Leveraging this formulation, we propose to compare SOM and SNE quantitatively on two datasets, and discuss possible avenues for future work to take advantage of both approaches.

Discrete variational auto-encoders (VAEs) are able to represent semantic latent spaces in generative learning. In many real-life settings, the discrete latent space consists of high-dimensional structures, and propagating gradients through the relevant structures often requires enumerating over an exponentially large latent space. Recently, various approaches were devised to propagate approximated gradients without enumerating over the space of possible structures. In this work, we use Natural Evolution Strategies (NES), a class of gradient-free black-box optimization algorithms, to learn discrete structured VAEs. The NES algorithms are computationally appealing as they estimate gradients with forward pass evaluations only, thus they do not require to propagate gradients through their discrete structures. We demonstrate empirically that optimizing discrete structured VAEs using NES is as effective as gradient-based approximations. Lastly, we prove NES converges for non-Lipschitz functions as appear in discrete structured VAEs.

Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for the definition of robust loss functions and scale-free functionals such as square-root Lasso. Standard approaches to deal with non-smoothness leverage either proximal splitting or coordinate descent. These approaches are effective but usually require parameter tuning, preconditioning or some sort of support pruning. In this work, we advocate and study a different route, which operates a non-convex but smooth over-parametrization of the underlying non-smooth optimization problems. This generalizes quadratic variational forms that are at the heart of the popular Iterative Reweighted Least Squares (IRLS). Our main theoretical contribution connects gradient descent on this reformulation to a mirror descent flow with a varying Hessian metric. This analysis is crucial to derive convergence bounds that are dimension-free. This explains the efficiency of the method when using small grid sizes in imaging. Our main algorithmic contribution is to apply the Variable Projection (VarPro) method which defines a new formulation by explicitly minimizing over part of the variables. This leads to a better conditioning of the minimized functional and improves the convergence of simple but very efficient gradient-based methods, for instance quasi-Newton solvers. We exemplify the use of this new solver for the resolution of regularized regression problems for inverse problems and supervised learning, including total variation prior and non-convex regularizers.

Patient similarity assessment, which identifies patients similar to a given patient, can help improve medical care. The assessment can be performed using Electronic Medical Records (EMRs). Patient similarity measurement requires converting heterogeneous EMRs into comparable formats to calculate their distance. While versatile document representation learning methods have been developed in recent years, it is still unclear how complex EMR data should be processed to create the most useful patient representations. This study presents a new data representation method for EMRs that takes the information in clinical narratives into account. To address the limitations of previous approaches in handling complex parts of EMR data, an unsupervised method is proposed for building a patient representation, which integrates unstructured data with structured data extracted from patients' EMRs. In order to model the extracted data, we employed a tree structure that captures the temporal relations of multiple medical events from EMR. We processed clinical notes to extract symptoms, signs, and diseases using different tools such as medspaCy, MetaMap, and scispaCy and mapped entities to the Unified Medical Language System (UMLS). After creating a tree data structure, we utilized two novel relabeling methods for the non-leaf nodes of the tree to capture two temporal aspects of the extracted events. By traversing the tree, we generated a sequence that could create an embedding vector for each patient. The comprehensive evaluation of the proposed method for patient similarity and mortality prediction tasks demonstrated that our proposed model leads to lower mean squared error (MSE), higher precision, and normalized discounted cumulative gain (NDCG) relative to baselines. Patient similarity analytics, Patient representation learning, Natural language processing, Health informatics 1 Introduction The patient similarity assessment identifies patients similar to a given patient. It allows physicians to gain insights into the records of matching patients and provide better treatments. Calculating patient similarity requires measuring the distance between patients within a population (1). A distance could be calculated based on various structured and unstructured data types in an electronic medical record (EMR). EMRs can be processed in the same way as general documents modeled as sequences of words. The difference is that EMRs are sequences of patient events, such as diagnoses, procedures, and medications. The representation of an EMR is a low-dimension and fixed-length embedding vector, so it can be used as an indicator to measure similarity between patients, simply like a representation of a document that can be applied to measure similarity between notes. Among previous works on patient representations based on EMRs, some have relied on structured data types (2-6), while others have only used unstructured data (7,8).