Forecasting irregularly sampled time series with missing values is a crucial task for numerous real-world applications such as healthcare, astronomy, and climate sciences. State-of-the-art approaches to this problem rely on Ordinary Differential Equations (ODEs) which are known to be slow and often require additional features to handle missing values. To address this issue, we propose a novel model using Graphs for Forecasting Irregularly Sampled Time Series with missing values which we call GraFITi. GraFITi first converts the time series to a Sparsity Structure Graph which is a sparse bipartite graph, and then reformulates the forecasting problem as the edge weight prediction task in the graph. It uses the power of Graph Neural Networks to learn the graph and predict the target edge weights. GraFITi has been tested on 3 real-world and 1 synthetic irregularly sampled time series dataset with missing values and compared with various state-of-the-art models. The experimental results demonstrate that GraFITi improves the forecasting accuracy by up to 17% and reduces the run time up to 5 times compared to the state-of-the-art forecasting models.

In this work, we develop machine learning algorithms for pricing used vehicles for B2B sales at Volkswagen Financial Services. The B2B pricing dataset is structured as Tabular data, however unlike commonly available tabular datasets, it is also time-indexed. To exploit the temporal component and improve prediction accuracy, we design a Sequential network that processes sequences of vehicles. We transform the data from a Tabular representation to a sequential representation by appending previously sold vehicles and their prices as additional features for a target vehicle to be priced. The sequential network, PriceNet, embeds each of the multiple vehicles through a dedicated Embedding module, and uses a series of Convolutional layers that learn sequential features relating to price trends and seasonalities. We show that PriceNet can improve performance over the state-of the-art deep-learning based Tabular baselines, Tab-Transformer and FT-Transformer.Additionally, this paper also covers related aspects such as Chronological Validation strategies for hyperparameter tuning models for time-indexed data. Notably, we also observed that Gradient Boosted Decision Tree algorithms, outperformed all the models in prediction accuracy. For this class of models, we therefore also designed a new Quantile level tuning approach that tunes the quantile level based on Out-of-sample chronological validation data. By tuning the quantile level, we can probabilistically determine whether to overshoot or undershoot in the case of temporal covariate shifts for out-of-sample testing data observed after the validation split.

In the early observation period of a time series, there might be only a few historic observations available to learn a model. However, in cases where an existing prior set of datasets is available, Meta learning methods can be applicable. In this paper, we devise a Meta learning method that exploits samples from additional datasets and learns to augment time series through adversarial learning as an auxiliary task for the target dataset. Our model (FEML), is equipped with a shared Convolutional backbone that learns features for varying length inputs from different datasets and has dataset specific heads to forecast for different output lengths. We show that FEML can meta learn across datasets and by additionally learning on adversarial generated samples as auxiliary samples for the target dataset, it can improve the forecasting performance compared to single task learning, and various solutions adapted from Joint learning, Multi-task learning and classic forecasting baselines.

We propose GQFormer, a probabilistic time series forecasting method that models the quantile function of the forecast distribution. Our methodology is rooted in the Implicit Quantile modeling approach, where samples from the Uniform distribution $\mathcal{U}\left( {0,1} \right)$ are reparameterized to quantile values of the target distribution. This allows implicit generative quantile modeling without any prior assumptions on the data distribution like Gaussianity, common in prior works. Our work is distinguished from prior quantile forecasting methods by novel methodological advances that relate to directly modeling the correlations among multiple quantile estimations at each forecasting horizon. To this end, we firstly develop a parameters haring architecture that implicitly models multiple quantile estimations efficiently and secondly regularize these through a novel multi-task loss function formulation that optimizes for quantile estimations to be sharper estimations individually and on the whole be spread maximally apart to capture the various modes of the underlying distribution. We experimentally validate the superiority of the method to state-of-the-art probabilistic forecasting baselines and ablations to the loss formulation.

In auction-based systems such as in used car centers and online auction websites, users usually bid on items, and those items get sold to their highest bidders. In these settings, every item is unique and can be sold only once, which means users’ purchase histories will be unique, and no common items will exist across them. On the other hand, items will not have any historical sales at all. Such extreme settings pose a significant challenge to the current recommender systems models that rely on historical user-item interactions. While some of those models will not be applicable altogether, such as the matrix factorization models, neighborhood models, and even the naive most-popular model, the rest will need to rely only on items’ attributes. In this paper, we address the challenges of auction-based item recommendation by proposing a simple multi-relational recommender model (MultiRec) that can seamlessly leverage user and item attributes along with auxiliary relational information such as the user’s bidding history. Experiments on one proprietary dataset from Volkswagen Financial Services used-cars center, and on a real-world publicly available eBay dataset show that the proposed model significantly outperforms multiple state-of-art models in the task of auction-based unique item recommendation.

Multi-task learning is an established approach for improving the generalization of a model. We explore multi-task learning in the context of time series forecasting. Specifically, we look into a multivariate setting where main and auxiliary series are to be forecasted for multi-step ahead. This results in an interesting multi-task learning problem formulation where the learning tasks come from future horizon of main and auxiliary series both. Our proposed method relies firstly on enumerating multiple Convolutional network architectures to balance the number of shared and non-shared layers between different time series tasks. Also, as multi-step strategies minimize forecast errors over the complete horizon, loss functions would be at different scales based on model uncertainty for near versus distant future. For this reason we propose a factorization of the weight vector for the learning tasks with respect to their categorization of belonging to main or auxiliary series and index in future. An optimal number of shared and non-shared layers together with a novel weighted loss, results in superior performance over 2 real-world datasets compared with several baselines.