Probabilistic time series forecasting involves estimating the distribution of future based on its history, which is essential for risk management in downstream decision-making. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks and the dependency is modeled by recurrent neural nets. We take the automatic relevance determination (ARD) view and devise a network to exploit the exogenous variables in addition to time series. In particular, our ARD network can incorporate the uncertainty of the exogenous variables and eventually helps identify useful exogenous variables and suppress those irrelevant for forecasting. The distribution of multi-step ahead forecasts are approximated by Monte Carlo simulation. We show in experiments that our model produces accurate and sharp probabilistic forecasts. The estimated uncertainty of our forecasting also realistically increases over time, in a spontaneous manner.

We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model represents the signal tensor of interest using a series of structured sign tensors. Unlike earlier methods, the sign series representation effectively addresses both low- and high-rank signals, while encompassing many existing tensor models -- including CP models, Tucker models, single index models, several hypergraphon models -- as special cases. We show that the sign tensor series is theoretically characterized, and computationally estimable, via classification tasks with carefully-specified weights. Excess risk bounds, estimation error rates, and sample complexities are established. We demonstrate the outperformance of our approach over previous methods on two datasets, one on human brain connectivity networks and the other on topic data mining.

In many cases, it is difficult to generate highly accurate models for time series data using a known parametric model structure. In response, an increasing body of research focuses on using neural networks to model time series approximately. A common assumption in training neural networks on time series is that the errors at different time steps are uncorrelated. However, due to the temporality of the data, errors are actually autocorrelated in many cases, which makes such maximum likelihood estimation inaccurate. In this paper, we propose to learn the autocorrelation coefficient jointly with the model parameters in order to adjust for autocorrelated errors. For time series regression, large-scale experiments indicate that our method outperforms the Prais-Winsten method, especially when the autocorrelation is strong. Furthermore, we broaden our method to time series forecasting and apply it with various state-of-the-art models. Results across a wide range of real-world datasets show that our method enhances performance in almost all cases.

Capacitated vehicle routing problem (CVRP) is being one of the most common optimization problems in our days, considering the wide usage of routing algorithms in multiple fields such as transportation domain, food delivery, network routing, ... Capacitated vehicle routing problem is classified as an NP-Hard problem, hence normal optimization algorithm can’t solve it. In our paper, we discuss a new way to solve the mentioned problem, using a recursive approach of the most known clustering algorithm “K-Means”, one of the known shortest path algorithm “Dijkstra”, and some mathematical operations. In this paper, we will show how to implement those methods together in order to get the nearest solution of the optimal route, since research and development are still on go, this research paper may be extended with another one, that will involve the implementational results of this thoric side.

Recent developments in Natural Language Processing (NLP) demonstrate that large-scale, self-supervised pre-training can be extremely beneficial for downstream tasks. These ideas have been adapted to other domains, including the analysis of the amino acid sequences of proteins. However, to date most attempts on protein sequences rely on direct masked language model style pre-training. In this work, we design a new, adversarial pre-training method for proteins, extending and specializing similar advances in NLP. We show compelling results in comparison to traditional MLM pre-training, though further development is needed to ensure the gains are worth the significant computational cost.

Time-series is ubiquitous across applications, such as transportation, finance and healthcare. Time-series is often influenced by external factors, especially in the form of asynchronous events, making forecasting difficult. However, existing models are mainly designated for either synchronous time-series or asynchronous event sequence, and can hardly provide a synthetic way to capture the relation between them. We propose Variational Synergetic Multi-Horizon Network (VSMHN), a novel deep conditional generative model. To learn complex correlations across heterogeneous sequences, a tailored encoder is devised to combine the advances in deep point processes models and variational recurrent neural networks. In addition, an aligned time coding and an auxiliary transition scheme are carefully devised for batched training on unaligned sequences. Our model can be trained effectively using stochastic variational inference and generates probabilistic predictions with Monte-Carlo simulation. Furthermore, our model produces accurate, sharp and more realistic probabilistic forecasts. We also show that modeling asynchronous event sequences is crucial for multi-horizon time-series forecasting.

Previous post-processing bias mitigation algorithms on both group and individual fairness don't work on regression models and datasets with multi-class numerical labels. We propose a priority-based post-processing bias mitigation on both group and individual fairness with the notion that similar individuals should get similar outcomes irrespective of socio-economic factors and more the unfairness, more the injustice. We establish this proposition by a case study on tariff allotment in a smart grid. Our novel framework establishes it by using a user segmentation algorithm to capture the consumption strategy better. This process ensures priority-based fair pricing for group and individual facing the maximum injustice. It upholds the notion of fair tariff allotment to the entire population taken into consideration without modifying the in-built process for tariff calculation. We also validate our method and show superior performance to previous work on a real-world dataset in criminal sentencing.

This article describes techniques employed in the production of a synthetic dataset of driver telematics emulated from a similar real insurance dataset. The synthetic dataset generated has 100,000 policies that included observations about driver's claims experience together with associated classical risk variables and telematics-related variables. This work is aimed to produce a resource that can be used to advance models to assess risks for usage-based insurance. It follows a three-stage process using machine learning algorithms. The first stage is simulating values for the number of claims as multiple binary classifications applying feedforward neural networks. The second stage is simulating values for aggregated amount of claims as regression using feedforward neural networks, with number of claims included in the set of feature variables. In the final stage, a synthetic portfolio of the space of feature variables is generated applying an extended $\texttt{SMOTE}$ algorithm. The resulting dataset is evaluated by comparing the synthetic and real datasets when Poisson and gamma regression models are fitted to the respective data. Other visualization and data summarization produce remarkable similar statistics between the two datasets. We hope that researchers interested in obtaining telematics datasets to calibrate models or learning algorithms will find our work valuable.

Dimension of the encoder output (i.e., the code layer) in an autoencoder is a key hyper-parameter for representing the input data in a proper space. This dimension must be carefully selected in order to guarantee the desired reconstruction accuracy. Although overcomplete representation can address this dimension issue, the computational complexity will increase with dimension. Inspired by non-parametric methods, here, we propose a metalearning approach to increase the number of basis vectors used in dynamic sparse coding on the fly. An actor-critic algorithm is deployed to automatically choose an appropriate dimension for feature vectors regarding the required level of accuracy. The proposed method benefits from online dictionary learning and fast iterative shrinkage-thresholding algorithm (FISTA) as the optimizer in the inference phase. It aims at choosing the minimum number of bases for the overcomplete representation regarding the reconstruction error threshold. This method allows for online controlling of both the representation dimension and the reconstruction error in a dynamic framework.

Sparse principal component analysis (PCA) is a popular tool for dimensional reduction of high-dimensional data. Despite its massive popularity, there is still a lack of theoretically justifiable Bayesian sparse PCA that is computationally scalable. A major challenge is choosing a suitable prior for the loadings matrix, as principal components are mutually orthogonal. We propose a spike and slab prior that meets this orthogonality constraint and show that the posterior enjoys both theoretical and computational advantages. Two computational algorithms, the PX-CAVI and the PX-EM algorithms, are developed. Both algorithms use parameter expansion to deal with the orthogonality constraint and to accelerate their convergence speeds. We found that the PX-CAVI algorithm has superior empirical performance than the PX-EM algorithm and two other penalty methods for sparse PCA. The PX-CAVI algorithm is then applied to study a lung cancer gene expression dataset. $\mathsf{R}$ package $\mathsf{VBsparsePCA}$ with an implementation of the algorithm is available on The Comprehensive R Archive Network.