Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic type. We study the stochastic multi-gradient (SMG) method, seen as an extension of the classical stochastic gradient method for single-objective optimization. At each iteration of the SMG method, a stochastic multi-gradient direction is calculated by solving a quadratic subproblem, and it is shown that this direction is biased even when all individual gradient estimators are unbiased. We establish rates to compute a point in the Pareto front, of order similar to what is known for stochastic gradient in both convex and strongly convex cases. The analysis handles the bias in the multi-gradient and the unknown a priori weights of the limiting Pareto point. The SMG method is framed into a Pareto-front type algorithm for the computation of the entire Pareto front. The Pareto-front SMG algorithm is capable of robustly determining Pareto fronts for a number of synthetic test problems. One can apply it to any stochastic MOO problem arising from supervised machine learning, and we report results for logistic binary classification where multiple objectives correspond to distinct-sources data groups.

Statistical models usually require vector representations of categorical variables, using for instance one-hot encoding. This strategy breaks down when the number of categories grows, as it creates high-dimensional feature vectors. Additionally, for string entries, one-hot encoding does not capture information in their representation.Here, we seek low-dimensional encoding of high-cardinality string categorical variables. Ideally, these should be: scalable to many categories; interpretable to end users; and facilitate statistical analysis. We introduce two encoding approaches for string categories: Gamma-Poisson matrix factorization on substring counts, and the min-hash encoder, for fast approximation of string similarities. We show that min-hash turns set inclusions into inequality relations that are easier to learn. Both approaches are scalable and streamable. Experiments on real and simulated data show that these methods improve supervised learning with high-cardinality categorical variables. We recommend the following: if scalability is central, the min-hash encoder is the best option as it does not require any data fit; if interpretability is important, the Gamma-Poisson factorization is the best alternative, as it can be interpreted as one-hot encoding on inferred categories with informative feature names. Both models enable autoML on the original string entries as they remove the need for feature engineering or data cleaning.

Automated machine learning (AutoML) systems are helpful data science assistants designed to scan data for novel features, select appropriate supervised learning models and optimize their parameters. For this purpose, Tree-based Pipeline Optimization Tool (TPOT) was developed using strongly typed genetic programing (GP) to recommend an optimized analysis pipeline for the data scientist's prediction problem. However, like other AutoML systems, TPOT may reach computational resource limits when working on big data such as whole-genome expression data. We introduce two new features implemented in TPOT that helps increase the system's scalability: Feature Set Selector (FSS) and Template. FSS provides the option to specify subsets of the features as separate datasets, assuming the signals come from one or more of these specific data subsets. FSS increases TPOT's efficiency in application on big data by slicing the entire dataset into smaller sets of features and allowing GP to select the best subset in the final pipeline. Template enforces type constraints with strongly typed GP and enables the incorporation of FSS at the beginning of each pipeline. Consequently, FSS and Template help reduce TPOT computation time and may provide more interpretable results. Our simulations show TPOT-FSS significantly outperforms a tuned XGBoost model and standard TPOT implementation.

Self-Organizing Maps (SOM), or Kohonen Networks ([1]), is an unsupervised learning method that can be applied to a wide range of problems such as: data visualization, dimensionality reduction or clustering. It was introduced in the 80' by computer scientist Teuvo Kohonen as a type of neural network ([Kohonen 82],[Kohonen 90]). In this post we are going to present the basics of the SOM model and build a minimal python implementation based on numpy. There is a huge litterature on SOMs (see [2]), theoretical and applied, this post only aims at having fun with this model over a tiny implementation. The approach is very much inspired by this post ([3]).

Gaussian processes are expressive, non-parametric statistical models that are well-suited to learn nonlinear dynamical systems. However, large-scale inference in these state space models is a challenging problem. In this paper, we propose CBF-SSM a scalable model that employs a structured variational approximation to maintain temporal correlations. In contrast to prior work, our approach applies to the important class of unstable systems, where state uncertainty grows unbounded over time. For these systems, our method contains a probabilistic, model-based backward pass that infers latent states during training. We demonstrate state-of-the-art performance in our experiments. Moreover, we show that CBF-SSM can be combined with physical models in the form of ordinary differential equations to learn a reliable model of a physical flying robotic vehicle.

A tacit assumption in linear regression is that (response, predictor)-pairs correspond to identical observational units. A series of recent works have studied scenarios in which this assumption is violated under terms such as ``Unlabeled Sensing and ``Regression with Unknown Permutation''. In this paper, we study the setup of multiple response variables and a notion of mismatches that generalizes permutations in order to allow for missing matches as well as for one-to-many matches. A two-stage method is proposed under the assumption that most pairs are correctly matched. In the first stage, the regression parameter is estimated by handling mismatches as contaminations, and subsequently the generalized permutation is estimated by a basic variant of matching. The approach is both computationally convenient and equipped with favorable statistical guarantees. Specifically, it is shown that the conditions for permutation recovery become considerably less stringent as the number of responses $m$ per observation increase. Particularly, for $m = \Omega(\log n)$, the required signal-to-noise ratio does no longer depend on the sample size $n$. Numerical results on synthetic and real data are presented to support the main findings of our analysis.

In recent years, the use of data-driven modelling and integration of behavioural and psychological factors in discrete choice and travel behaviour analysis have become active areas of research [2, 3, 4]. In the context of data-driven models, behavioural variations describe the correlation between observed choice attributes and unobserved socioeconomic factors using a flexible and tractable model specification. These variations include: decision-protocols, choice sets, unobserved taste variations and unobserved attributes [5]. Under these considerations, recent studies on travel behaviour analysis have so far primarily focused on representing heterogeneity in the error correction function and incorporating it into utility based multinomial logit (MNL) models [3]. Models such as mixed multinomial logit (MMNL) or latent class (LC) model offers flexibility in representing heterogeneity and substitution patterns. In addition, recent conceptual frameworks such as the integrated choice and latent variable (ICLV) use individuals' psychometric indicators to represent unobserved behavioural and perception heterogeneity [6]. It is also possible to apply a generative machine learning to identify informative latent constructs in travel decision making without subjective behaviour indicators [7, 8]. However, the true underlying behavioural patterns are often unknown and usually approximated by some predetermined exogenous indicator variables that would often lead to model misspecification due to lack of complete information, or error in data collection [9]. Furthermore, accurate specification of the underlying distribution assumes individuals have access to all available information regarding the travel activity (e.g.

This work studies the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is motivated by the recently proposed linear transforms based tensor-tensor product and tensor SVD. We define a new transforms depended tensor rank and the corresponding tensor nuclear norm. Then we solve the TRPCA problem by convex optimization whose objective is a weighted combination of the new tensor nuclear norm and the $\ell_1$-norm. In theory, we show that under certain incoherence conditions, the convex program exactly recovers the underlying low-rank and sparse components. It is of great interest that our new TRPCA model generalizes existing works. In particular, if the studied tensor reduces to a matrix, our TRPCA model reduces to the known matrix RPCA. Our new TRPCA which is allowed to use general linear transforms can be regarded as an extension of our former TRPCA work which uses the discrete Fourier transform. But their proof of the recovery guarantee is different. Numerical experiments verify our results and the application on image recovery demonstrates the superiority of our method.

Stress research is a rapidly emerging area in thefield of electroencephalography (EEG) based signal processing.The use of EEG as an objective measure for cost effective andpersonalized stress management becomes important in particularsituations such as the non-availability of mental health facilities.In this study, long-term stress is classified using baseline EEGsignal recordings. The labelling for the stress and control groupsis performed using two methods (i) the perceived stress scalescore and (ii) expert evaluation. The frequency domain featuresare extracted from five-channel EEG recordings in addition tothe frontal and temporal alpha and beta asymmetries. The alphaasymmetry is computed from four channels and used as a feature.Feature selection is also performed using a t-test to identifystatistically significant features for both stress and control groups.We found that support vector machine is best suited to classifylong-term human stress when used with alpha asymmetry asa feature. It is observed that expert evaluation based labellingmethod has improved the classification accuracy up to 85.20%.Based on these results, it is concluded that alpha asymmetry maybe used as a potential bio-marker for stress classification, when labels are assigned using expert evaluation.

Automatic detection of emotion has the potential to revolutionize mental health and wellbeing. Recent work has been successful in predicting affect from unimodal electrocardiogram (ECG) data. However, to be immediately relevant for real-world applications, physiology-based emotion detection must make use of ubiquitous photoplethysmogram (PPG) data collected by affordable consumer fitness trackers. Additionally, applications of emotion detection in healthcare settings will require some measure of uncertainty over model predictions. We present here a Bayesian deep learning model for end-to-end classification of emotional valence, using only the unimodal heartbeat time series collected by a consumer fitness tracker (Garmin V\'ivosmart 3). We collected a new dataset for this task, and report a peak F1 score of 0.7. This demonstrates a practical relevance of physiology-based emotion detection `in the wild' today.