Learning disentangled representations for time series is a promising path to facilitate reliable generalization to in- and out-of distribution (OOD), offering benefits like feature derivation and improved interpretability and fairness, thereby enhancing downstream tasks. We focus on disentangled representation learning for home appliance electricity usage, enabling users to understand and optimize their consumption for a reduced carbon footprint. Our approach frames the problem as disentangling each attribute's role in total consumption. Unlike existing methods assuming attribute independence which leads to non-identiability, we acknowledge real-world time series attribute correlations, learned up to a smooth bijection using contrastive learning and a single autoencoder. To address this, we propose a Disentanglement under Independence-Of-Support via Contrastive Learning (DIOSC), facilitating representation generalization across diverse correlated scenarios. Our method utilizes innovative \textit{l}-variational inference layers with self-attention, effectively addressing temporal dependencies across bottom-up and top-down networks. We find that DIOSC can enhance the task of representation of time series electricity consumption. We introduce TDS (Time Disentangling Score) to gauge disentanglement quality. TDS reliably reflects disentanglement performance, making it a valuable metric for evaluating time series representations disentanglement. Code available at https://institut-polytechnique-de-paris.github.io/time-disentanglement-lib.

Recent works in Variational Inference have examined alternative criteria to the commonly used exclusive Kullback-Leibler divergence. Encouraging empirical results have been obtained with the family of alpha-divergences, but few works have focused on the asymptotic properties of the proposed algorithms, especially as the number of iterations goes to infinity. In this paper, we study a procedure that ensures a monotonic decrease in the alpha-divergence. We provide sufficient conditions to guarantee its convergence to a local minimizer of the alpha-divergence at a geometric rate when the variational family belongs to the class of exponential models. The sample-based version of this ideal procedure involves biased gradient estimators, thus hindering any theoretical study. We propose an alternative unbiased algorithm, we prove its almost sure convergence to a local minimizer of the alpha-divergence, and a law of the iterated logarithm. Our results are exemplified with toy and real-data experiments.

In this paper, we introduce a novel family of iterative algorithms which carry out $\alpha$-divergence minimisation in a Variational Inference context. They do so by ensuring a systematic decrease at each step in the $\alpha$-divergence between the variational and the posterior distributions. In its most general form, the variational distribution is a mixture model and our framework allows us to simultaneously optimise the weights and components parameters of this mixture model. Our approach permits us to build on various methods previously proposed for $\alpha$-divergence minimisation such as Gradient or Power Descent schemes and we also shed a new light on an integrated Expectation Maximization algorithm. Lastly, we provide empirical evidence that our methodology yields improved results on several multimodal target distributions and on a real data example.

To address functional-output regression, we introduce projection learning (PL), a novel dictionary-based approach that learns to predict a function that is expanded on a dictionary while minimizing an empirical risk based on a functional loss. PL makes it possible to use non orthogonal dictionaries and can then be combined with dictionary learning; it is thus much more flexible than expansion-based approaches relying on vectorial losses. This general method is instantiated with reproducing kernel Hilbert spaces of vector-valued functions as kernel-based projection learning (KPL). For the functional square loss, two closed-form estimators are proposed, one for fully observed output functions and the other for partially observed ones. Both are backed theoretically by an excess risk analysis. Then, in the more general setting of integral losses based on differentiable ground losses, KPL is implemented using first-order optimization for both fully and partially observed output functions. Eventually, several robustness aspects of the proposed algorithms are highlighted on a toy dataset; and a study on two real datasets shows that they are competitive compared to other nonlinear approaches. Notably, using the square loss and a learnt dictionary, KPL enjoys a particularily attractive trade-off between computational cost and performances.

This paper addresses the detection of a stochastic process in noise from a finite sample under various sampling schemes. We consider two hypotheses. The noise only hypothesis amounts to model the observations as a sample of a i.i.d. Gaussian random variables (noise only). The signal plus noise hypothesis models the observations as the samples of a continuous time stationary Gaussian process (the signal) taken at known but random time-instants and corrupted with an additive noise. Two binary tests are considered, depending on which assumptions is retained as the null hypothesis. Assuming that the signal is a linear combination of the solution of a multidimensional stochastic differential equation (SDE), it is shown that the minimum Type II error probability decreases exponentially in the number of samples when the False Alarm probability is fixed. This behavior is described by error exponents that are completely characterized. It turns out that they are related to the asymptotic behavior of the Kalman Filter in random stationary environment, which is studied in this paper. Finally, numerical illustrations of our claims are provided in the context of sensor networks.

This paper deals with the detection of a continuous random process described by an Ornstein-Uhlenbeck (O-U) stochastic differential equation. Randomly spaced sensors or equivalently a random time sampler which deliver noisy samples of the process are used for this detection. Two types of tests are considered: either H0 refers to the presence of the noisy O-U process or H0 refers to the sole presence of noise. For any fixed false alarm probability, it is shown that the type II error probability decreases to zero exponentially in the number of samples. The exponents, which do not depend on the false alarm probability, are characterized. This work completes former contributions that consider noiseless O-U process with a random sampling or noisy O-U processes with a regular sampling.

We consider the problem of pile-ups occurring in gamma spectrometry signals for HPGe detectors. The temporal signal is transformed in a sequence of busy and idle periods, each busy period being characterized by its duration and its associated energy. We present an estimator to correct the pile-up phenomenon, based on an analytical formula. Applications on simulations and real spectrometrical signals are presented, which show good adequation between what we wish to retrieve and the estimation