Efficient Smoothed Concomitant Lasso Estimation for High Dimensional Regression

In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods, the Lasso being a canonical example, are popular candidates to address high dimension. For efficiency, they rely on tuning a parameter trading data fitting versus sparsity. For the Lasso theory to hold this tuning parameter should be proportional to the noise level, yet the latter is often unknown in practice. A possible remedy is to jointly optimize over the regression parameter as well as over the noise level. This has been considered under several names in the literature: Scaled-Lasso, Square-root Lasso, Concomitant Lasso estimation for instance, and could be of interest for confidence sets or uncertainty quantification. In this work, after illustrating numerical difficulties for the Smoothed Concomitant Lasso formulation, we propose a modification we coined Smoothed Concomitant Lasso, aimed at increasing numerical stability. We propose an efficient and accurate solver leading to a computational cost no more expansive than the one for the Lasso. We leverage on standard ingredients behind the success of fast Lasso solvers: a coordinate descent algorithm, combined with safe screening rules to achieve speed efficiency, by eliminating early irrelevant features

Learning to Estimate Driver Drowsiness from Car Acceleration Sensors using Weakly Labeled Data

This paper addresses the learning task of estimating driver drowsiness from the signals of car acceleration sensors. Since even drivers themselves cannot perceive their own drowsiness in a timely manner unless they use burdensome invasive sensors, obtaining labeled training data for each timestamp is not a realistic goal. To deal with this difficulty, we formulate the task as a weakly supervised learning. We only need to add labels for each complete trip, not for every timestamp independently. By assuming that some aspects of driver drowsiness increase over time due to tiredness, we formulate an algorithm that can learn from such weakly labeled data. We derive a scalable stochastic optimization method as a way of implementing the algorithm. Numerical experiments on real driving datasets demonstrate the advantages of our algorithm against baseline methods.Comment: Accepted by ICASSP202

Sparse Regression with Multi-type Regularized Feature Modeling

Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such as Lasso regression for (continuous) predictors treated as linear effects. However, many predictive problems involve different types of predictors and require a tailored regularization term. We propose a multi-type Lasso penalty that acts on the objective function as a sum of subpenalties, one for each type of predictor. As such, we allow for predictor selection and level fusion within a predictor in a data-driven way, simultaneous with the parameter estimation process. We develop a new estimation strategy for convex predictive models with this multi-type penalty. Using the theory of proximal operators, our estimation procedure is computationally efficient, partitioning the overall optimization problem into easier to solve subproblems, specific for each predictor type and its associated penalty. Earlier research applies approximations to non-differentiable penalties to solve the optimization problem. The proposed SMuRF algorithm removes the need for approximations and achieves a higher accuracy and computational efficiency. This is demonstrated with an extensive simulation study and the analysis of a case-study on insurance pricing analytics

Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (i.e., walking, sitting, running). However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Furthermore, interpreting the resulting clusters is difficult, especially when the data is high-dimensional. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through alternating minimization, using a variation of the expectation maximization (EM) algorithm. We derive closed-form solutions to efficiently solve the two resulting subproblems in a scalable way, through dynamic programming and the alternating direction method of multipliers (ADMM), respectively. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile sensor dataset how TICC can be used to learn interpretable clusters in real-world scenarios.Comment: This revised version fixes two small typos in the published versio