arXiv subjects

Sandjai Bhulai

Publications and source records attributed to Sandjai Bhulai.

27 records · Page 2Linked to original sources

arXiv2021

The Generalized Cascade Click Model: A Unified Framework for Estimating Click Models

Given the vital importance of search engines to find digital information, there has been much scientific attention on how users interact with search engines, and how such behavior can be modeled. Many models on user - search engine interaction, which in the literature are known as click models, come in the form of Dynamic Bayesian Networks. Although many authors have used the resemblance between the different click models to derive estimation procedures for these models, in particular in the form of expectation maximization (EM), still this commonly requires considerable work, in particular when it comes to deriving the E-step. What we propose in this paper, is that this derivation is commonly unnecessary: many existing click models can in fact, under certain assumptions, be optimized as they were Input-Output Hidden Markov Models (IO-HMMs), for which the forward-backward equations immediately provide this E-step. To arrive at that conclusion, we will present the Generalized Cascade Model (GCM) and show how this model can be estimated using the IO-HMM EM framework, and provide two examples of how existing click models can be mapped to GCM. Our GCM approach to estimating click models has also been implemented in the gecasmo Python package.

cs.IR↗

arXiv2021

Invertible DenseNets with Concatenated LipSwish

We introduce Invertible Dense Networks (i-DenseNets), a more parameter efficient extension of Residual Flows. The method relies on an analysis of the Lipschitz continuity of the concatenation in DenseNets, where we enforce invertibility of the network by satisfying the Lipschitz constant. Furthermore, we propose a learnable weighted concatenation, which not only improves the model performance but also indicates the importance of the concatenated weighted representation. Additionally, we introduce the Concatenated LipSwish as activation function, for which we show how to enforce the Lipschitz condition and which boosts performance. The new architecture, i-DenseNet, out-performs Residual Flow and other flow-based models on density estimation evaluated in bits per dimension, where we utilize an equal parameter budget. Moreover, we show that the proposed model out-performs Residual Flows when trained as a hybrid model where the model is both a generative and a discriminative model.

stat.ML↗

arXiv2021

Jasmine: A New Active Learning Approach to Combat Cybercrime

Over the past decade, the advent of cybercrime has accelarated the research on cybersecurity. However, the deployment of intrusion detection methods falls short. One of the reasons for this is the lack of realistic evaluation datasets, which makes it a challenge to develop techniques and compare them. This is caused by the large amounts of effort it takes for a cyber analyst to classify network connections. This has raised the need for methods (i) that can learn from small sets of labeled data, (ii) that can make predictions on large sets of unlabeled data, and (iii) that request the label of only specially selected unlabeled data instances. Hence, Active Learning (AL) methods are of interest. These approaches choose specific unlabeled instances by a query function that are expected to improve overall classification performance. The resulting query observations are labeled by a human expert and added to the labeled set. In this paper, we propose a new hybrid AL method called Jasmine. Firstly, it determines how suitable each observation is for querying, i.e., how likely it is to enhance classification. These properties are the uncertainty score and anomaly score. Secondly, Jasmine introduces dynamic updating. This allows the model to adjust the balance between querying uncertain, anomalous and randomly selected observations. To this end, Jasmine is able to learn the best query strategy during the labeling process. This is in contrast to the other AL methods in cybersecurity that all have static, predetermined query functions. We show that dynamic updating, and therefore Jasmine, is able to consistently obtain good and more robust results than querying only uncertainties, only anomalies or a fixed combination of the two.

cs.CR↗

arXiv2021

Personalized Stopping Rules in Bayesian Adaptive Mastery Assessment

We propose a new model to assess the mastery level of a given skill efficiently. The model, called Bayesian Adaptive Mastery Assessment (BAMA), uses information on the accuracy and the response time of the answers given and infers the mastery at every step of the assessment. BAMA balances the length of the assessment and the certainty of the mastery inference by employing a Bayesian decision-theoretic framework adapted to each student. All these properties contribute to a novel approach in assessment models for intelligent learning systems. The purpose of this research is to explore the properties of BAMA and evaluate its performance concerning the number of questions administered and the accuracy of the final mastery estimates across different students. We simulate student performances and establish that the model converges with low variance and high efficiency leading to shorter assessment duration for all students. Considering the experimental results, we expect our approach to avoid the issue of over-practicing and under-practicing and facilitate the development of Learning Analytics tools to support the tutors in the evaluation of learning effects and instructional decision making.

math.OC↗

arXiv2021

Invertible DenseNets

We introduce Invertible Dense Networks (i-DenseNets), a more parameter efficient alternative to Residual Flows. The method relies on an analysis of the Lipschitz continuity of the concatenation in DenseNets, where we enforce the invertibility of the network by satisfying the Lipschitz constraint. Additionally, we extend this method by proposing a learnable concatenation, which not only improves the model performance but also indicates the importance of the concatenated representation. We demonstrate the performance of i-DenseNets and Residual Flows on toy, MNIST, and CIFAR10 data. Both i-DenseNets outperform Residual Flows evaluated in negative log-likelihood, on all considered datasets under an equal parameter budget.

cs.LG↗

arXiv2020

A roundabout model with on-ramp queues: exact results and scaling approximations

This paper introduces a general model of a single-lane roundabout, represented as a circular lattice that consists of $L$ cells, with Markovian traffic dynamics. Vehicles enter the roundabout via on-ramp queues that have stochastic arrival processes, remain on the roundabout a random number of cells, and depart via off-ramps. Importantly, the model does not oversimplify the dynamics of traffic on roundabouts, while various performance-related quantities (such as delay and queue length) allow an analytical characterization. In particular, we present an explicit expression for the marginal stationary distribution of each cell on the lattice. Moreover, we derive results that give insight on the dependencies between parts of the roundabout, and on the queue distribution. Finally, we find scaling limits that allow, for every partition of the roundabout in segments, to approximate 1) the joint distribution of the occupation of these segments by a multivariate Gaussian distribution; and 2) the joint distribution of their total queue lengths by a collection of independent Poisson random variables. To verify the scaling limit statements, we develop a novel way to empirically assess convergence in distribution of random variables.

nlin.CG↗

arXiv2017

Optimal Pricing under Mixed Logit Choice

In this paper we consider the problem of pricing multiple differentiated products. This is challenging as a price change in one product, not only changes the demand of that particular product, but also the demand for the other products. To address this problem, customer choice models have recently been introduced as these are capable of describing customer choice behavior across differentiated products. In the present paper the objective is to obtain the revenue-maximizing prices when the customer's decision making process is modelled according to a particular customer choice model, namely the mixed logit model. The main advantage of using the mixed logit model, also known as the random coefficients logit model, for this purpose is its flexibility. In the single-product case we establish log-concavity of the optimization problem under certain regularity conditions. In addition, in the multi-product case, we present the results of our extensive numerical experiments. These suggest that the mixed logit model, by taking unobserved customer heterogeneity and flexible substitution patterns into account, can significantly improve the attainable revenue.

math.OC↗

arXiv2015

Modeling trend progression through an extension of the Polya Urn Process

Knowing how and when trends are formed is a frequently visited research goal. In our work, we focus on the progression of trends through (social) networks. We use a random graph (RG) model to mimic the progression of a trend through the network. The context of the trend is not included in our model. We show that every state of the RG model maps to a state of the Polya process. We find that the limit of the component size distribution of the RG model shows power-law behaviour. These results are also supported by simulations.

cs.SI↗

arXiv2015

Modelling of trends in Twitter using retweet graph dynamics

In this paper we model user behaviour in Twitter to capture the emergence of trending topics. For this purpose, we first extensively analyse tweet datasets of several different events. In particular, for these datasets, we construct and investigate the retweet graphs. We find that the retweet graph for a trending topic has a relatively dense largest connected component (LCC). Next, based on the insights obtained from the analyses of the datasets, we design a mathematical model that describes the evolution of a retweet graph by three main parameters. We then quantify, analytically and by simulation, the influence of the model parameters on the basic characteristics of the retweet graph, such as the density of edges and the size and density of the LCC. Finally, we put the model in practice, estimate its parameters and compare the resulting behavior of the model to our datasets.

cs.SI↗