Frequent episode mining is a popular method for discovering temporal dependencies in symbolic time series data. In frequent pattern mining, it is important to assess statistical significance of discovered patterns so as to be able to discard unimportant patterns. In the literature, statistical significance is assessed through a hypothesis testing framework where the null hypothesis models data with no important patterns. Most currently available methods for frequent episode mining can handle only an iid null hypothesis. Since the data is a time series, it is desirable to deal with a null hypothesis that also allows for simple temporal dependencies. In this paper we present a method to characterize the distribution of non-overlapped occurrences of an episode and hence to assess its significance under a Markovian null hypothesis. This is the first such result. We illustrate the effectiveness of the method through simulations.

Recurrent neural networks (RNNs) have been a very popular predictive modelling choice for sequence based applications. Here we consider RNNs for time series forecasting. The proposed distinct architecture is based on Seq2Seq OR encoder-decoder (ED) framework, capturing (stochastic) seasonal correlations intelligently with accurate multi-step forecasting ability. We derive our nonlinear architecture from the classic linear multiplicative seasonal auto-regressive model. Unlike existing RNN approaches, it (i)places equal emphasis on each cycle of input window, (ii)contains vanishing gradients and (iii)has accurate multi-step forecast feature in the presence (or absence) of exogenous inputs. It can be used on both single or multiple sequence data. For the multiple sequence case, we also propose a novel greedy recursive procedure to build (one or more) predictive models across sequences when per-sequence data is less. Our experiments demonstrate the utility of our proposed architecture both in single and multiple sequence scenarios.

Missing data scenarios are very common in ML applications in general and time-series/sequence applications are no exceptions. This paper pertains to a novel Recurrent Neural Network (RNN) based solution for sequence prediction under missing data. Our method is distinct from all existing approaches. It tries to encode the missingness patterns in the data directly without trying to impute data either before or during model building. Our encoding is lossless and achieves compression. It can be employed for both sequence classification and forecasting. We focus on forecasting here in a general context of multi-step prediction in presence of possible exogenous inputs. In particular, we propose novel variants of Encoder-Decoder (Seq2Seq) RNNs for this. The encoder here adopts the above mentioned pattern encoding, while at the decoder which has a different structure, multiple variants are feasible. We demonstrate the utility of our proposed architecture via multiple experiments on both single and multiple sequence (real) data-sets. We consider both scenarios where (i)data is naturally missing and (ii)data is synthetically masked.

Public transport buses suffer travel time uncertainties owing to diverse factors such as dwell times at bus stops, signals, seasonal variations and fluctuating travel demands etc. Traffic in the developing world in particular is afflicted by additional factors like lack of lane discipline, diverse modes of transport and excess vehicles. The bus travel time prediction problem on account of these factors continues to remain a demanding problem especially in developing countries. The current work proposes a method to address bus travel time prediction in real-time. The central idea of our method is to recast the dynamic prediction problem as a value-function prediction problem under a suitably constructed Markov reward process (MRP). Once recast as an MRP, we explore a family of value-function predictors using temporal-difference (TD) learning for bus prediction. Existing approaches build supervised models either by (a)training based on travel time targets only between successive bus-stops while keeping the no. of models linear in the number of bus-stops OR (b)training a single model which predicts between any two bus-stops while ignoring the huge variation in the travel-time targets during training. Our TD-based approach attempts to strike an optimal balance between the above two class of approaches by training with travel-time targets between any two bus-stops while keeping the number of models (approximately) linear in the number of bus-stops. It also keeps a check on the variation in the travel-time targets. Our extensive experimental results vindicate the efficacy of the proposed method. The method exhibits comparable or superior prediction performance on mid-length and long-length routes compared to the state-of-the art.

Public transport buses have uncertainties associated with its arrival/travel times, due to several factors such as signals, dwell times at bus stops, seasonal variations, fluctuating travel demands, and so on. In the developing world, these uncertainties are further magnified by the presence of excess vehicles, diverse modes of transport, and acute lack of lane discipline. Hence, the problem of bus arrival time prediction continues to be a challenging one especially in developing countries. This paper proposes a new methodology for bus arrival time prediction in real time. Unlike existing approaches, the proposed method explicitly learns the spatial (and temporal) correlations/patterns of traffic in a novel fashion. Specifically, it first detects the unknown order of spatial dependence and then learns linear, non-stationary spatial correlations for this detected order. It learns temporal correlations between successive trips as a function of their time difference. To make the optimal prediction feasible, the learnt predictive model is rewritten in a suitable linear state-space form, and then, an appropriate Kalman filter (KF) is applied. The performance was evaluated with real field data and compared with existing methods.

Public transport buses exhibit uncertainties in their arrival/travel times, due to several factors such as signals, dwell times at bus stops, seasonal variations, fluctuating travel demands etc. Further, factors like excess vehicles, acute lack of lane discipline and diversity in modes of transport additionally plague the traffic in the developing world. Owing to these diverse factors, the bus arrival time prediction (BATP) continues to be a challenging problem especially in the developing world. The current work proposes a data-driven method to perform bus arrival time prediction in real-time. Unlike existing approaches, the proposed method explicitly learns both the spatial and temporal correlations/patterns of traffic in a novel and general fashion. In particular, it first detects the unknown order of spatial dependence and then learns general nonlinear and non-stationary correlations using supervised learning, for this detected order. The real time prediction problem is now posed as an inference problem on an associated non-linear dynamical system (NLDS) model. We propose to use an Extended Kalman Filter (EKF) to solve this inference problem in an approximate but efficient manner. We demonstrate the effectiveness of our proposed algorithm on real field data from challenging traffic conditions in the developing world. Our experiments demonstrate that the proposed EKF outperforms diverse existing state-of-art data driven approaches proposed for the same problem.

Predicting travel times of vehicles in urban settings is a useful and tangible quantity of interest in the context of intelligent transportation systems. We address the problem of travel time prediction in arterial roads using data sampled from probe vehicles. There is only a limited literature on methods using data input from probe vehicles. The spatio-temporal dependencies captured by existing data driven approaches are either too detailed or very simplistic. We strike a balance of the existing data driven approaches to account for varying degrees of influence a given road may experience from its neighbors, while controlling the number of parameters to be learnt. Specifically, we use a NoisyOR conditional probability distribution (CPD) in conjunction with a dynamic Bayesian network (DBN) to model state transitions of various roads. We propose an efficient algorithm to learn model parameters. We also propose an algorithm for predicting travel times on trips of arbitrary durations. Using synthetic and real world data traces we demonstrate the superior performance of the proposed method under different traffic conditions.

The rapid accumulation of microarray data translates into an urgent need for tools to perform integrative microarray analysis. Integrative Array Analyzer is a comprehensive analysis and visualization software toolkit, which aims to facilitate the reuse of the large amount of cross-platform and cross-species microarray data. It is composed of the data preprocess module, the co-expression analysis module, the differential expression analysis module, the functional and transcriptional annotation module and the graph visualization module.