This paper addresses the problem of time series forecasting for non-stationary signals and multiple future steps prediction. To handle this challenging task, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective function for training deep neural networks. DILATE aims at accurately predicting sudden changes, and explicitly incorporates two terms supporting precise shape and temporal change detection. We introduce a differentiable loss function suitable for training deep neural nets, and provide a custom back-prop implementation for speeding up optimization. We also introduce a variant of DILATE, which provides a smooth generalization of temporally-constrained Dynamic TimeWarping (DTW). Experiments carried out on various non-stationary datasets reveal the very good behaviour of DILATE compared to models trained with the standard Mean Squared Error (MSE) loss function, and also to DTW and variants. DILATE is also agnostic to the choice of the model, and we highlight its benefit for training fully connected networks as well as specialized recurrent architectures, showing its capacity to improve over state-of-the-art trajectory forecasting approaches.

This paper addresses the problem of time series forecasting for non-stationary signals and multiple future steps prediction. To handle this challenging task, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective function for training deep neural networks. DILATE aims at accurately predicting sudden changes, and explicitly incorporates two terms supporting precise shape and temporal change detection. We introduce a differentiable loss function suitable for training deep neural nets, and provide a custom back-prop implementation for speeding up optimization. We also introduce a variant of DILATE, which provides a smooth generalization of temporally-constrained Dynamic TimeWarping (DTW).

In this work, the novel Image Transformation Sequence Retrieval (ITSR) task is presented, in which a model must retrieve the sequence of transformations between two given images that act as source and target, respectively. Given certain characteristics of the challenge such as the multiplicity of a correct sequence or the correlation between consecutive steps of the process, we propose a solution to ITSR using a general model-based Reinforcement Learning such as Monte Carlo Tree Search (MCTS), which is combined with a deep neural network. Our experiments provide a benchmark in both synthetic and real domains, where the proposed approach is compared with supervised training. The results report that a model trained with MCTS is able to outperform its supervised counterpart in both the simplest and the most complex cases. Our work draws interesting conclusions about the nature of ITSR and its associated challenges.

This paper addresses learning end-to-end models for time series data that include a temporal alignment step via dynamic time warping (DTW). Existing approaches to differentiable DTW either differentiate through a fixed warping path or apply a differentiable relaxation to the min operator found in the recursive steps used to solve the DTW problem. We instead propose a DTW layer based around bi-level optimisation and deep declarative networks, which we name DecDTW. By formulating DTW as a continuous, inequality constrained optimisation problem, we can compute gradients for the solution of the optimal alignment (with respect to the underlying time series) using implicit differentiation. An interesting byproduct of this formulation is that DecDTW outputs the optimal warping path between two time series as opposed to a soft approximation, recoverable from Soft-DTW. We show that this property is particularly useful for applications where downstream loss functions are defined on the optimal alignment path itself. This naturally occurs, for instance, when learning to improve the accuracy of predicted alignments against ground truth alignments. We evaluate DecDTW on two such applications, namely the audio-to-score alignment task in music information retrieval and the visual place recognition task in robotics, demonstrating state-of-the-art results in both.

This paper addresses the problem of multi-step time series forecasting for non-stationary signals that can present sudden changes. Current state-of-the-art deep learning forecasting methods, often trained with variants of the MSE, lack the ability to provide sharp predictions in deterministic and probabilistic contexts. To handle these challenges, we propose to incorporate shape and temporal criteria in the training objective of deep models. We define shape and temporal similarities and dissimilarities, based on a smooth relaxation of Dynamic Time Warping (DTW) and Temporal Distortion Index (TDI), that enable to build differentiable loss functions and positive semi-definite (PSD) kernels. With these tools, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective for deterministic forecasting, that explicitly incorporates two terms supporting precise shape and temporal change detection. For probabilistic forecasting, we introduce STRIPE++ (Shape and Time diverRsIty in Probabilistic forEcasting), a framework for providing a set of sharp and diverse forecasts, where the structured shape and time diversity is enforced with a determinantal point process (DPP) diversity loss. Extensive experiments and ablations studies on synthetic and real-world datasets confirm the benefits of leveraging shape and time features in time series forecasting.

This paper addresses the problem of time series forecasting for non-stationary signals and multiple future steps prediction. To handle this challenging task, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective function for training deep neural networks. DILATE aims at accurately predicting sudden changes, and explicitly incorporates two terms supporting precise shape and temporal change detection. We introduce a differentiable loss function suitable for training deep neural nets, and provide a custom back-prop implementation for speeding up optimization. We also introduce a variant of DILATE, which provides a smooth generalization of temporally-constrained Dynamic TimeWarping (DTW).

A new study has found that patterns of pupil dilation can reveal when two minds'connect.' Using eye-tracking technology, researchers have found collective pupillary synchrony between speakers and listeners were greatest during emotional peaks of a narrative – and decreased as the story became less engaging. The results of the experiments have suggested that speakers who are highly expressive are more likely to evoke pupillary synchrony - allowing them to keep their audiences's attention. Pupil dilation can occur during many different settings. When you enter a dark cinema, your pupils will automatically dilate to let more light in.