Thus, it is natural to endow each state with a distribution over the tokens it may emit.

The importance of considering contextual probabilities in shaping response patterns within psychological testing is underscored, despite the ubiquitous nature of order effects discussed extensively in methodological literature. Drawing from concepts such as path-dependency, first-order autocorrelation, state-dependency, and hysteresis, the present study is an attempt to address how earlier responses serve as an anchor for subsequent answers in tests, surveys, and questionnaires. Introducing the notion of non-commuting observables derived from quantum physics, I highlight their role in characterizing psychological processes and the impact of measurement instruments on participants' responses. We advocate for the utilization of first-order Markov chain modeling to capture and forecast sequential dependencies in survey and test responses. The employment of the first-order Markov chain model lies in individuals' propensity to exhibit partial focus to preceding responses, with recent items most likely exerting a substantial influence on subsequent response selection. This study contributes to advancing our understanding of the dynamics inherent in sequential data within psychological research and provides a methodological framework for conducting longitudinal analyses of response patterns of test and questionnaire.

We encapsulate an individual daily trajectory as a sequence of tokens by adding unique time interval tokens to the location tokens. Using the architecture of an autoregressive language model, GPT-2, this sequence of tokens is trained from scratch, allowing us to construct a deep learning model that sequentially generates an individual daily trajectory. Environmental factors such as meteorological conditions and individual attributes such as gender and age are symbolized by unique special tokens, and by training these tokens and trajectories on the GPT-2 architecture, we can generate trajectories that are influenced by both environmental factors and individual attributes.

Natural language processing (NLP) and deep learning are growing in popularity for their use in ML technologies like self-driving cars and speech recognition software. As more companies begin to implement deep learning components and other machine learning practices, the demand for software developers and data scientists with proficiency in deep learning is skyrocketing. Today, we will introduce you to a popular deep learning project, the Text Generator, to familiarize you with important, industry-standard NLP concepts, including Markov chains. By the end of this article, you'll understand how to build a Text Generator component for search engine systems and the know-how to implement Markov chains for faster predictive models. Text generation is popular across the board and in every industry, especially for the mobile, app, and data science.

Predicting and modeling human behavior and finding trends within human decision-making process is a major social sciences'problem. Rock Paper Scissors (RPS) is the fundamental strategic question in many game theory problems and real-world competitions. Finding the right approach to beat a particular human opponent is challenging. Here we use Markov Chains with set chain lengths as the single AIs (artificial intelligences) to compete against humans in iterated RPS game. This is the first time that an AI algorithm is applied in RPS human competition behavior studies. We developed an architecture of multi-AI with changeable parameters to adapt to different competition strategies. We introduce a parameter "focus length" (an integer of e.g. 5 or 10) to control the speed and sensitivity for our multi-AI to adapt to the opponent's strategy change. We experimented with 52 different people, each playing 300 rounds continuously against one specific multi-AI model, and demonstrated that our strategy could win over more than 95% of human opponents.

Assortment optimization is an important problem that arises in many practical applications such as retailing and online advertising where the goal is to find a subset of products from a universe of substitutable products that maximize a seller's expected revenue. The demand and the revenue depend on the substitution behavior of the customers that is captured by a choice model. One of the key challenges is to find the right model for the customer substitution behavior. Many parametric random utility based models have been considered in the literature to capture substitution. However, in all these models, the probability of purchase increases as we add more options to the assortment. This is not true in general and in many settings, the probability of purchase may decrease if we add more products to the assortment, referred to as the choice overload. In this paper we attempt to address these serious limitations and propose a generalization of the Markov chain based choice model considered in Blanchet et al. In particular, we handle dynamic preferences and the choice overload phenomenon using a Markovian comparison model that is a generalization of the Markovian substitution framework of Blanchet et al. The Markovian comparison framework allows us to implicitly model the search cost in the choice process and thereby, modeling both dynamic preferences as well as the choice overload phenomenon. We consider the assortment optimization problem for the special case of our generalized Markov chain model where the underlying Markov chain is rank-1 (this is a generalization of the Multinomial Logit model). We show that the assortment optimization problem under this model is NP-hard and present a fully polynomial-time approximation scheme (FPTAS) for this problem.

We show the equivalence of discrete choice models and the class of binary choice forests, which are random forest based on binary choice trees. This suggests that standard machine learning techniques based on random forest can serve to estimate discrete choice model with an interpretable output. This is confirmed by our data driven result that states that random forest can accurately predict the choice probability of any discrete choice model. Our framework has unique advantages: it can capture behavioral patterns such as irrationality or sequential searches; it handles nonstandard formats of training data that result from aggregation; it can measure product importance based on how frequently a random customer would make decisions depending on the presence of the product; it can also incorporate price information. Our numerical results show that binary choice forest can outperform the best parametric models with much better computational times.

Abstract-- Extremely preterm infants commonly require intubation and invasive mechanical ventilation after birth. While the duration of mechanical ventilation should be minimized in order to avoid complications, extubation failure is associated with increases in morbidities and mortality. As part of a prospective observational study aimed at developing an accurate predictor of extubation readiness, Markov and semi-Markov chain models were applied to gain insight into the respiratory patterns of these infants, with more robust timeseries modeling using semi-Markov models. This model revealed interesting similarities and differences between newborns who succeeded extubation and those who failed. The parameters of the model were further applied to predict extubation readiness via generative (joint likelihood) and discriminative (support vector machine) approaches. Results showed that up to 84% of infants who failed extubation could have been accurately identified prior to extubation.

Trajectory prediction (TP) is of great importance for a wide range of location-based applications in intelligent transport systems such as location-based advertising, route planning, traffic management, and early warning systems. In the last few years, the widespread use of GPS navigation systems and wireless communication technology enabled vehicles has resulted in huge volumes of trajectory data. The task of utilizing this data employing spatio-temporal techniques for trajectory prediction in an efficient and accurate manner is an ongoing research problem. Existing TP approaches are limited to short-term predictions. Moreover, they cannot handle a large volume of trajectory data for long-term prediction. To address these limitations, we propose a scalable clustering and Markov chain based hybrid framework, called Traj-clusiVAT-based TP, for both short-term and long-term trajectory prediction, which can handle a large number of overlapping trajectories in a dense road network. In addition, Traj-clusiVAT can also determine the number of clusters, which represent different movement behaviours in input trajectory data. In our experiments, we compare our proposed approach with a mixed Markov model (MMM)-based scheme, and a trajectory clustering, NETSCAN-based TP method for both short- and long-term trajectory predictions. We performed our experiments on two real, vehicle trajectory datasets, including a large-scale trajectory dataset consisting of 3.28 million trajectories obtained from 15,061 taxis in Singapore over a period of one month. Experimental results on two real trajectory datasets show that our proposed approach outperforms the existing approaches in terms of both short- and long-term prediction performances, based on prediction accuracy and distance error (in km).