The present paper explores a novel variant of Random Indexing (RI) based representations for encoding language data with a view to using them in a dynamic scenario where events are happening in a continuous fashion. As the size of the representations in the general method of onehot encoding grows linearly with the size of the vocabulary, they become non-scalable for online purposes with high volumes of dynamic data. On the other hand, existing pre-trained embedding models are not suitable for detecting happenings of new events due to the dynamic nature of the text data. The present work addresses this issue by using a novel RI representation by imposing a probability distribution on the number of randomized entries which leads to a class of RI representations. It also provides a rigorous analysis of the goodness of the representation methods to encode semantic information in terms of the probability of orthogonality. Building on these ideas we propose an algorithm that is log-linear with the size of vocabulary to track the semantic relationship of a query word to other words for suggesting the events that are relevant to the word in question. We ran simulations using the proposed algorithm for tweet data specific to three different events and present our findings. The proposed probabilistic RI representations are found to be much faster and scalable than Bag of Words (BoW) embeddings while maintaining accuracy in depicting semantic relationships.
Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We devise a new strategy that avoids partitioning the vector space and present a novel randomized algorithm that runs in time linear in dimensionality of the space and sub-linear in the intrinsic dimensionality and the size of the dataset and takes space constant in dimensionality of the space and linear in the size of the dataset. The proposed algorithm allow…
We consider the problem of probabilistic forecasting over categories with graph structure, where the dynamics at a vertex depends on its local connectivity structure. We present GOPHER, a method that combines the inductive bias of graph neural networks with neural ODEs to capture the intrinsic local continuous-time dynamics of our probabilistic forecasts. We study the benefits of these two inductive biases by comparing against baseline models that help disentangle the benefits of each. We find that capturing the graph structure is crucial for accurate in-domain probabilistic predictions and mo…
ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations
Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Vanderbilt University（范德堡大学）；National Institute on Aging（美国国家衰老研究所）
Probabilistic atlases provide essential spatial contextual information for image interpretation, Bayesian modeling, and algorithmic processing. Such atlases are typically constructed by grouping subjects with similar demographic information. Importantly, use of the same scanner minimizes inter-group variability. However, generalizability and spatial specificity of such approaches is more limited than one might like. Inspired by Commowick "Frankenstein's creature paradigm" which builds a personal specific anatomical atlas, we propose a data-driven framework to build a personal specific probabil…
Universitat Politècnica de València（瓦伦西亚理工大学）；Universitat de Valéncia（瓦伦西亚大学）；Centro de Estudios Superiores Felipe II（费利佩二世高等研究中心）
In this paper, we present a computational technique to deal with uncertainty in dynamic continuous models in Social Sciences. Considering data from surveys, the method consists of determining the probability distribution of the survey output and this allows to sample data and fit the model to the sampled data using a goodness-of-fit criterion based on the chi-square-test. Taking the fitted parameters non-rejected by the chi-square-test, substituting them into the model and computing their outputs, we build 95% confidence intervals in each time instant capturing uncertainty of the survey data (…
Automatic Construction of Pattern Classifiers Capable of Continuous Incremental Learning and Unlearning Tasks Based on Compact-Sized Probabilistic Neural Network
Department of Computer Engineering, College of Science & Technology（计算机工程系，科学与技术学院）
We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions on the unknown transition rate matrix. The resulting estimator is a set of transition rate matrices that, for reasons of conjugacy, is easy to find. To determine the hyperparameters for our set of priors, we reconsider the problem in discrete time, where we can use the well-known Imprecise Dirichlet Model. In particular, we show how the limit of …
Neural-symbolic AI (NeSy) allows neural networks to exploit symbolic background knowledge in the form of logic. It has been shown to aid learning in the limited data regime and to facilitate inference on out-of-distribution data. Probabilistic NeSy focuses on integrating neural networks with both logic and probability theory, which additionally allows learning under uncertainty. A major limitation of current probabilistic NeSy systems, such as DeepProbLog, is their restriction to finite probability distributions, i.e., discrete random variables. In contrast, deep probabilistic programming (DPP…
University of California, Berkeley（加州大学伯克利分校）；Arizona State University（亚利桑那州立大学）；Vicarious Inc.（维卡里奥公司）；Carnegie Mellon University（卡内基梅隆大学）
Despite the recent successes of probabilistic programming languages (PPLs) in AI applications, PPLs offer only limited support for random variables whose distributions combine discrete and continuous elements. We develop the notion of measure-theoretic Bayesian networks (MTBNs) and use it to provide more general semantics for PPLs with arbitrarily many random variables defined over arbitrary measure spaces. We develop two new general sampling algorithms that are provably correct under the MTBN framework: the lexicographic likelihood weighting (LLW) for general MTBNs and the lexicographic parti…
Multivariate time series prediction has attracted a lot of attention because of its wide applications such as intelligence transportation, AIOps. Generative models have achieved impressive results in time series modeling because they can model data distribution and take noise into consideration. However, many existing works can not be widely used because of the constraints of functional form of generative models or the sensitivity to hyperparameters. In this paper, we propose ScoreGrad, a multivariate probabilistic time series forecasting framework based on continuous energy-based generative m…
Shanghai Jiao Tong University（上海交通大学）；Technical University of Denmark（丹麦技术大学）
We present a data-driven approach for probabilistic wind power forecasting based on conditional normalizing flow (CNF). In contrast with the existing, this approach is distribution-free (as for non-parametric and quantile-based approaches) and can directly yield continuous probability densities, hence avoiding quantile crossing. It relies on a base distribution and a set of bijective mappings. Both the shape parameters of the base distribution and the bijective mappings are approximated with neural networks. Spline-based conditional normalizing flow is considered owing to its non-affine charac…
University of Edinburgh（爱丁堡大学）；Alan Turing Institute（艾伦·图灵研究所）
The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives in logic programming, which is now increasingly seen to provide a declarative background to complex machine learning applications. While many systems offer inference capabilities, the more significant challenge is that of learning meaningful and interpretable symbolic representations from data. In that regard, inductive logic programming and related technique…
Continuous-time event sequences, i.e., sequences consisting of continuous time stamps and associated event types ("marks"), are an important type of sequential data with many applications, e.g., in clinical medicine or user behavior modeling. Since these data are typically modeled autoregressively (e.g., using neural Hawkes processes or their classical counterparts), it is natural to ask questions about future scenarios such as "what kind of event will occur next" or "will an event of type $A$ occur before one of type $B$". Unfortunately, some of these queries are notoriously hard to address s…
User modeling plays an important role in delivering customized web services to the users and improving their engagement. However, most user models in the literature do not explicitly consider the temporal behavior of users. More recently, continuous-time user modeling has gained considerable attention and many user behavior models have been proposed based on temporal point processes. However, typical point process based models often considered the impact of peer influence and content on the user participation and neglected other factors. Gamification elements, are among those factors that are …
We propose a new framework of XGBoost that predicts the entire conditional distribution of a univariate response variable. In particular, XGBoostLSS models all moments of a parametric distribution (i.e., mean, location, scale and shape [LSS]) instead of the conditional mean only. Choosing from a wide range of continuous, discrete and mixed discrete-continuous distribution, modelling and predicting the entire conditional distribution greatly enhances the flexibility of XGBoost, as it allows to gain additional insight into the data generating process, as well as to create probabilistic forecasts…
We propose a new framework of CatBoost that predicts the entire conditional distribution of a univariate response variable. In particular, CatBoostLSS models all moments of a parametric distribution (i.e., mean, location, scale and shape [LSS]) instead of the conditional mean only. Choosing from a wide range of continuous, discrete and mixed discrete-continuous distributions, modelling and predicting the entire conditional distribution greatly enhances the flexibility of CatBoost, as it allows to gain insight into the data generating process, as well as to create probabilistic forecasts from w…
