{"title": "A Probabilistic Model for Online Document Clustering with Application to Novelty Detection", "book": "Advances in Neural Information Processing Systems", "page_first": 1617, "page_last": 1624, "abstract": null, "full_text": "     A Probabilistic Model for Online Document\nClustering with Application to Novelty Detection\n\n\n\n              Jian Zhang                           Zoubin Ghahramani\n     School of Computer Science            Gatsby Computational Neuroscience Unit\n      Cargenie Mellon University                   University College London\n         Pittsburgh, PA 15213                       London WC1N 3AR, UK\n     jian.zhang@cs.cmu.edu                     zoubin@gatsby.ucl.ac.uk\n\n\n                                      Yiming Yang\n                              School of Computer Science\n                                 Cargenie Mellon University\n                                    Pittsburgh, PA 15213\n                                  yiming@cs.cmu.edu\n\n\n\n\n                                        Abstract\n\n         In this paper we propose a probabilistic model for online document clus-\n         tering. We use non-parametric Dirichlet process prior to model the grow-\n         ing number of clusters, and use a prior of general English language\n         model as the base distribution to handle the generation of novel clusters.\n         Furthermore, cluster uncertainty is modeled with a Bayesian Dirichlet-\n         multinomial distribution. We use empirical Bayes method to estimate\n         hyperparameters based on a historical dataset. Our probabilistic model\n         is applied to the novelty detection task in Topic Detection and Tracking\n         (TDT) and compared with existing approaches in the literature.\n\n\n\n1    Introduction\n\nThe task of online document clustering is to group documents into clusters as long as\nthey arrive in a temporal sequence. Generally speaking, it is difficult for several reasons:\nFirst, it is unsupervised learning and the learning has to be done in an online fashion,\nwhich imposes constraints on both strategy and efficiency. Second, similar to other learning\nproblems in text, we have to deal with a high-dimensional space with tens of thousands of\nfeatures. And finally, the number of clusters can be as large as thousands in newswire data.\n\nThe objective of novelty detection is to identify the novel objects from a sequence of data,\nwhere \"novel\" is usually defined as dissimilar to previous seen instances. Here we are inter-\nested in novelty detection in the text domain, where we want to identify the earliest report\nof every new event in a sequence of news stories. Applying online document clustering\nto the novelty detection task is straightforward by assigning the first seed of every cluster\nas novel and all its remaining ones as non-novel. The most obvious application of novelty\ndetection is that, by detecting novel events, systems can automatically alert people when\nnew events happen, for example.\n\n\f\nIn this paper we apply Dirichlet process prior to model the growing number of clusters, and\npropose to use a General English language model as a basis of newly generated clusters.\nIn particular, the new clusters will be generated according to the prior and a background\nGeneral English model, and each document cluster is modeled using a Bayesian Dirichlet-\nmultinomial language model. The Bayesian inference can be easily carried out due to\nconjugacy, and model hyperparameters are estimated using a historical dataset by the em-\npirical Bayes method. We evaluate our online clustering algorithm (as well as its variants)\non the novelty detection task in TDT, which has been regarded as the hardest task in that\nliterature [2].\n\nThe rest of this paper is organized as follows. We first introduce our probabilistic model\nin Section 2, and in Section 3 we give detailed information on how to estimate model\nhyperparameters. We describe the experiments in Section 4, and related work in Section 5.\nWe conclude and discuss future work in Section 6.\n\n\n2      A Probabilistic Model for Online Document Clustering\n\nIn this section we will describe the generative probabilistic model for online document\n\nclustering. We use x = (n(x)\n                               1    , n(x)\n                                      2       , . . . , n(x)) to represent a document vector where each\n                                                            V\nelement n(x)\n           v       denotes the term frequency of the vth corresponding word in the document\nx, and V is the total size of the vocabulary.\n\n\n2.1    Dirichlet-Multinomial Model\n\nThe multinomial distribution has been one of the most frequently used language models for\nmodeling documents in information retrieval. It assumes that given the set of parameters\n = (1, 2, . . . , V ), a document x is generated with the following probability:\n                                                  (      V       n(x)            V\n                                p(                                    v    )!\n                                    x|) =               v=1                          n(x)\n                                                                                            v\n                                                         V                             v         .\n                                                                 n(x)\n                                                         v=1          v    ! v=1\nFrom the formula we can see the so-called naive assumption: words are assumed to be in-\ndependent of each other. Given a collection of documents generated from the same model,\nthe parameter  can be estimated with Maximum Likelihood Estimation (MLE).\n\nIn a Bayesian approach we would like to put a Dirichlet prior over the parameter ( \nDir()) such that the probability of generating a document is obtained by integrating over\nthe parameter space: p(x) =                p(|)p(x|)d. This integration can be easily written\ndown due to the conjugacy between Dirichlet and multinomial distributions. The key dif-\nference between the Bayesian approach and the MLE is that the former uses a distribution\nto model the uncertainty of the parameter , while the latter gives only a point estimation.\n\n\n2.2    Online Document Clustering with Dirichlet Process Mixture Model\n\nIn our system documents are grouped into clusters in an online fashion. Each cluster is\nmodeled with a multinomial distribution whose parameter  follows a Dirichlet prior. First,\na cluster is chosen based on a Dirichlet process prior (can be either a new or existing\ncluster), and then a document is drawn from that cluster.\n\nWe use Dirichlet Process (DP) to model the prior distribution of 's, and our hierarchical\nmodel is as follows:\n                                      xi|ci                     M ul(.|(ci))\n                                            i         iid.\n                                                                G                                    (1)\n                                            G                   DP (, G0)\n\n\f\nwhere ci is the cluster indicator variable, i is the multinomial parameter 1 for each docu-\nment, and (ci) is the unique  for the cluster ci. G is a random distribution generated from\nthe Dirichlet process DP (, G0) [4], which has a precision parameter  and a base distribu-\ntion G0. Here our base distribution G0 is a Dirichlet distribution Dir(1, 2, . . . , V )\nwith        V      \n            t=1         t = 1, which reflects our expected knowledge about G. Intuitively, our G0\ndistribution can be treated as the prior over general English word frequencies, which has\nbeen used in information retrieval literature [6] to model general English documents.\n\nThe exact cluster-document generation process can be described as follows:\n\n         1. Let xi be the current document under processing (the ith document in the input\n             sequence), and C1, C2, . . . , Cm are already generated clusters.\n\n         2. Draw a cluster ci based on the following Dirichlet process prior [4]:\n                                                                   |C\n                             p(c                                         j |\n                                    i = Cj )           =                                     (j = 1, 2, . . . , m)\n                                                             +     m           |C\n                                                                    j=1               j |\n                                                                                                                                (2)\n                          p(ci = Cm+1) =                     +     m           |C\n                                                                    j=1               j |\n             where |Cj| stands for the cardinality of cluster j with                                      m      |C\n                                                                                                          j=1          j | = i - 1, and\n             with certain probability a new cluster Cm+1 will be generated.\n\n         3. Draw the document xi from the cluster ci.\n\n\n2.3      Model Updating\n\nOur models for each cluster need to be updated based on incoming documents. We can\nwrite down the probability that the current document xi is generated by any cluster as\n\n            p(xi|Cj) =               p((Cj)|Cj)p(xi|(Cj))d(Cj) (j = 1, 2, . . . , m, m + 1)\n\nwhere p((Cj)|Cj) is the posterior distribution of parameters of the jth cluster (j =\n1, 2, . . . , m) and we use p((Cm+1)|Cm+1) = p((Cm+1)) to represent the prior distribu-\ntion of the parameters of the new cluster for convenience. Although the dimensionality of\n is high (V  105 in our case), closed-form solution can be obtained under our Dirichlet-\nmultinomial assumption. Once the conditional probabilities p(xi|Cj) are computed, the\nprobabilities p(Cj|xi) can be easily calculated using the Bayes rule:\n\n                                                                   p(C\n                                       p(                                  j )p(xi|Cj )\n                                         Cj|xi) =             m+1 p(C\n                                                              j =1                j )p(xi|Cj )\n\nwhere the prior probability of each cluster is calculated using equation (2).\n\nNow there are several choices we can consider on how to update the cluster models. The\nfirst choice, which is correct but obviously intractable, is to fork m + 1 children of the\ncurrent system where the jth child is updated with document xi assigned to cluster j, while\nthe final system is a probabilistic combination of those children with the corresponding\nprobabilities p(Cj|xi). The second choice is to make a hard decision by assigning the\ncurrent document xi to the cluster with the maximum probability:\n\n                                                                                 p(Cj)p(xi|Cj)\n                             ci = arg max p(Cj|xi) =                                                             .\n                                             C                                  m+1\n                                                  j                                     p(C\n                                                                                j =1           j )p(xi|Cj )\n\n       1For  we use v to denote the vth element in the vector, i to denote the parameter vector that\ngenerates the ith document, and (j) to denote the parameter vector for the jth cluster.\n\n\f\nThe third choice is to use a soft probabilistic updating, which is similar in spirit to the\nAssumed Density Filtering (ADF) [7] in the literature. That is, each cluster is updated by\nexponentiating the likelihood function with probabilities:\n\n                                                                            p(Cj |xi)\n                       p((Cj)|xi, Cj)               p(xi|(Cj))                        p((Cj)|Cj)\n\nHowever, we have to specially deal with the new cluster since we cannot afford both time-\nwise and space-wise to generate a new cluster for each incoming document. Instead, we\nwill update all existing clusters as above, and new cluster will be generated only if ci =\nCm+1. We will use HD and PD (hard decision and probabilistic decision) to denote the\nlast two candidates in our experiments.\n\n\n3     Learning Model Parameters\n\nIn the above probabilistic model there are still several hyperparameters not specified,\nnamely the  and  in the base distribution G0 = Dir(1, 2, . . . , V ), and the pre-\ncision parameter  in the DP (, G0). Since we can obtain a partially labeled historical\ndataset 2 , we now discuss how to estimate those parameters respectively.\n\nWe will mainly use the empirical Bayes method [5] to estimate those parameters instead\nof taking a full Bayesian approach, since it is easier to compute and generally reliable\nwhen the number of data points is relatively large compared to the number of parameters.\nBecause the i's are iid. from the random distribution G, by integrating out the G we get\n\n                                                                                  1\n                       i|1, 2, . . . , i-1                        G                                  \n                                                     + i - 1 0 +  + i - 1                                    j\n                                                                                                   j<i\n\nwhere the distribution is a mixture of continuous and discrete distributions, and the \ndenotes the probability measure giving point mass to .\n\nNow suppose we have a historical dataset H which contains K labeled clusters Hj(j =\n1, 2, . . . , K), with the kth cluster Hk = {xk,1, xk,2, . . . , xk,m } having m\n                                                                                              k                             k documents.\nThe joint probability of 's of all documents can be obtained as\n\n                                               |H|                                      1\n                  p(1, 2, . . . , |H|) =           (                G                                       \n                                                            + i - 1 0 +  + i - 1                                  j )\n                                               i=1                                                  j<i\n\nwhere |H| is the total number of documents. By integrating over the unknown parameter\n's we can get\n\n                                |H|                \n           p(H)         =        p(xi|i)\n                                  i=1               p(1,2,...,|H|)d1d2...d|H|\n                             |H|                                                  1\n                        =                                              G                                  \n                                                       + i - 1 0 +  + i - 1                                   j )di\n                             i=1  p(xi|i)(                                                       j<i                              (3)\nEmpirical Bayes method can be applied to equation (3) to estimate the model parameters\nby maximization3. In the following we discuss how to estimate parameters individually in\ndetail.\n\n     2Although documents are grouped into clusters in the historical dataset, we cannot make directly\nuse of those labels due to the fact that clusters in the test dataset are different from those in the\nhistorical dataset.\n     3Since only a subset of documents are labeled in the historical dataset H, the maximization is\nonly taken over the union of the labeled clusters.\n\n\f\n3.1         Estimating t's\n\nOur hyperparameter  vector contains V number of parameters for the base distribution G0,\nwhich can be treated as the expected distribution of G  the prior of the cluster parameter\n's.\n\nAlthough  contains V  105 number of actual parameters in our case, we can still use\nthe empirical Bayes to do a reliable point estimation since the amount of data we have to\nrepresent general English is large (in our historical dataset there are around 106 documents,\naround 1.8  108 English words in total) and highly informative about . We use the\nsmoothed estimation   (1 + n(H)\n                                              1    , 1 + n(H)\n                                                             2         , . . . , 1 + n(H)) where n(H)                                  n(x)\n                                                                                           V              t      =             xH       t\nis the total number of times that term t happened in the collection H, and                                           V         \n                                                                                                                     t=1            t should\nbe normalized to 1. Furthermore, the pseudo-count one is added to alleviate the out-of-\nvocabulary problem.\n\n\n3.2         Estimating \n\nThough  is just a scalar parameter, it has the effect to control the uncertainty of the prior\nknowledge about how clusters are related to the general English model with the parameter\n. We can see that  controls how far each new cluster can deviate from the general English\nmodel 4. It can be estimated as follows:\n\n                                   K                                     K\n               ^\n                = arg max                p(Hk|) = arg max                         p(Hk|(k))p((k)|)d(k)                             (4)\n                                                                 \n                                   k=1                                  k=1\n\n^\n can be numerically computed by solving the following equation:\n\n                       V                      K       V                                         K               V\nK() - K                    (v)v +                    (v + n(Hk)\n                                                                              v     )v -              ( +           n(Hk)\n                                                                                                                          v          ) = 0\n                      v=1                    k=1 v=1                                            k=1             v=1\n\nwhere the digamma function (x) is defined as (x)  d ln (x).\n                                                                                          dx\n\nAlternatively we can choose  by evaluating over the historical dataset. This is applicable\n(though computationally expensive) since it is only a scalar parameter and we can pre-\ncompute its possible range based on equation (4).\n\n\n3.3         Estimating \n\nThe precision parameter  of the DP is also very important for the model, which controls\nhow far the random distribution G can deviate from the baseline model G0. In our case, it is\nalso the prior belief about how quickly new clusters will be generated in the sequence. Sim-\nilarly we can use equation (3) to estimate , since items related to  can be factored out as\n     |H|      yi    . Suppose we have a labeled subset H L = {(x\n     i=1 +i-1                                                                             1, y1), (x2, y2), . . . , (xM , yM )}\nof training data, where yi is 1 if xi is a novel document or 0 otherwise. Here we describe\ntwo possible choices:\n\n            1. The simplest way is to assume that  is a fixed constant during the process, and it\n               can be computed as ^\n                                            = arg max                             yt\n                                                                                          , here HL denotes the subset of\n                                                                       iHL +i-1\n               indices of labeled documents in the whole sequence.\n\n            2. The assumption that  is fixed maybe restrictive in reality, especially considering\n               the fact that it reflects the generation rate of new clusters. More generally, we\n\n       4The mean and variance of a Dirichlet distribution (1, 2, . . . , V )  Dir(1, 2, . . . , V )\nare: E[v] = v and Var[v] = v(1-v) .\n                                             (+1)\n\n\f\n             can assume that  is some function of variable i. In particular, we assume  =\n             a/i + b + ci where a, b and c are non-negative numbers. This formulation is a\n             generalization of the above case, where the i-1 term allows a much faster decrease\n             at the beginning, and c is the asymptotic rate of events happening as i  .\n             Again the parameters a, b and c are estimated by MLE over the training dataset:\n             ^\n             a, ^b, ^\n                   c = arg max                       (a/i+b+ci)yi\n                                     a,b,c>0                         .\n                                                iHL a/i+b+ci+i\n\n\n4       Experiments\n\nWe apply the above online clustering model to the novelty detection task in Topic Detection\nand Tracking (TDT). TDT has been a research community since its 1997 pilot study, which\nis a research initiative that aims at techniques to automatically process news documents in\nterms of events. There are several tasks defined in TDT, and among them Novelty Detection\n(a.k.a. First Story Detection or New Event Detection) has been regarded as the hardest task\nin this area [2]. The objective of the novelty detection task is to detect the earliest report\nfor each event as soon as that report arrives in the temporal sequence of news stories.\n\n\n4.1      Dataset\n\nWe use the TDT2 corpus as our historical dataset for estimating parameters, and use the\nTDT3 corpus to evaluate our model 5. Notice that we have a subset of documents in the\nhistorical dataset (TDT2) for which events labels are given. The TDT2 corpus used for\nnovelty detection task consists of 62,962 documents, among them 8,401 documents are\nlabeled in 96 clusters. Stopwords are removed and words are stemmed, and after that there\nare on average 180 words per document. The total number of features (unique words) is\naround 100,000.\n\n\n4.2      Evaluation Measure\n\nIn our experiments we use the standard TDT evaluation measure [1] to evaluate our results.\nThe performance is characterized in terms of the probability of two types of errors: miss\nand false alarm (PMiss and PF A). These two error probabilities are then combined into a\nsingle detection cost, Cdet, by assigning costs to miss and false alarm errors:\n\n                    Cdet = CMiss  PMiss  Ptarget + CF A  PF A  Pnon-target\n\nwhere\n\n         1. CMiss and CF A are the costs of a miss and a false alarm, respectively,\n\n         2. PMissand PF A are the conditional probabilities of a miss and a false alarm, re-\n             spectively, and\n\n         3. Ptarget and Pnon-target is the priori target probabilities (Ptarget = 1 -\n             Pnon-target).\n\nIt is the following normalized cost that is actually used in evaluating various TDT systems:\n\n                                                             C\n                         (C                                       det\n                               det)norm = min(CMiss  Ptarget, CFA  Pnon-target)\n\nwhere the denominator is the minimum of two trivial systems. Besides, two types of eval-\nuations are used in TDT, namely macro-averaged (topic-weighted) and micro-averaged\n\n       5Strictly speaking we only used the subsets of TDT2 and TDT3 that is designated for the novelty\ndetection task.\n\n\f\n(story-weighted) evaluations. In macro-averaged evaluation, the cost is computed for every\nevent, and then the average is taken. In micro-averaged evaluation the cost is averaged over\nall documents' decisions generated by the system, thus large event will have bigger impact\non the overall performance. Note that macro-averaged evaluation is used as the primary\nevaluation measure in TDT. In addition to the binary decision \"novel\" or \"non-novel\", each\nsystem is required to generated a confidence score for each test document. The higher the\nscore is, the more likely the document is novel. Here we mainly use the minimum cost to\nevaluate systems by varying the threshold, which is independent of the threshold setting.\n\n\n4.3      Methods\n\nOne simple but effective method is the \"GAC-INCR\" clustering method [9] with cosine\nsimilarity metric and TFIDF term weighting, which has remained to be the top performing\nsystem in TDT 2002 & 2003 official evaluations. For this method the novelty confidence\nscore we used is one minus the similarity score between the current cluster xi and its nearest\nneighbor cluster: s(xi) = 1.0 - maxj<i sim(ci, cj), where ci and cj are the clusters that\nxi and xj are assigned to, respectively, and the similarity is taken to be the cosine similarity\nbetween two cluster vectors, where the ltc TFIDF term weighting scheme is used to scale\neach dimension of the vector. Our second method is to train a logistic regression model\nwhich combines multiple features generated by the GAC-INCR method. Those features\nnot only include the similarity score used by the first method, but also include the size of\nits nearest cluster, the time difference between the current cluster and the nearest cluster,\netc. We call this method \"Logistic Regression\", where we use the posterior probability\np(novelty|xi) as the confidence score. Finally, for our online clustering algorithm we\nchoose the quantity s(xi) = log p(C0|xi) as the output confidence score.\n\n\n4.4      Experimental Results\n\nOur results for three methods are listed in Table 1, where both macro-averaged and micro-\naveraged minimum normalized costs are reported 6. The GAC-INCR method performs\nvery well, so does the logistic regression method. For our DP results, we observed that\nusing the optimized ^\n                           will get results (not listed in the table) that are around 10% worse\nthan using the  obtained through validation, which might be due to the flatness of the\noptimal function value as well as the sample bias of the clusters in the historical dataset7.\nAnother observation is that the probabilistic decision does not actually improve the hard\ndecision performance, especially for the var option. Generally speaking, our DP methods\nare comparable to the other two methods, especially in terms of topic-weighted measure.\n\n\n                       Table 1: Results for novelty detection on TDT3 corpus\n\n                                       Topic-weighted Cost            Story-weighted Cost\n                   Method                COST (Miss, FA)                COST (Miss, FA)\n                GAC-INCR              0.6945 (0.5614, 0.0272)        0.7090 (0.5614, 0.0301)\n            Logistic Regression       0.7027 (0.5732, 0.0264)        0.6911 (0.5732, 0.0241)\n             DP with fix, HD         0.7054 (0.4737, 0.0473)        0.7744 (0.5965, 0.0363)\n             DP with var, HD         0.6901 (0.5789, 0.0227)        0.7541 (0.5789, 0.0358)\n             DP with fix, PD         0.7054 (0.4737, 0.0473)        0.7744 (0.5965, 0.0363)\n             DP with var, PD         0.9025 (0.8772, 0.0052)        0.9034 (0.8772, 0.0053)\n\n       6In TDT official evaluation there is also the DET curve, which is similar in spirit to the ROC curve\nthat can reflects how the performance changes as the threshold varies. We will report those results in\na longer version of this paper.\n       7It is known that the cluster labeling process of LDC is biased toward topics that will be covered\nin multiple languages instead of one single language.\n\n\f\n5      Related Work\n\nZaragoza et al. [11] applied a Bayesian Dirichlet-multinomial model to the ad hoc infor-\nmation retrieval task and showed that it is comparable to other smoothed language models.\nBlei et al. [3] used Chinese Restaurant Processes to model topic hierachies for a collec-\ntion of documents. West et al. [8] discussed the sampling techniques for base distribution\nparameters in the Dirichlet process mixture model.\n\n\n6      Conclusions and Future Work\n\nIn this paper we used a hierarchical probabilistic model for online document clustering.\nWe modeled the generation of new clusters with a Dirichlet process mixture model, where\nthe base distribution can be treated as the prior of general English model and the precision\nparameter is closely related to the generation rate of new clusters. Model parameters are\nestimated with empirical Bayes and validation over the historical dataset. Our model is\nevaluated on the TDT novelty detection task, and results show that our method is promising.\n\nIn future work we would like to investigate other ways of estimating parameters and use\nsampling methods to revisit previous cluster assignments. We would also like to apply our\nmodel to the retrospective detection task in TDT where systems do not need to make de-\ncisions online. Though its simplicity, the unigram multinomial model has its well-known\nlimitation, which is the naive assumption about word independence. We also plan to ex-\nplore richer but still tractable language models in this framework. Meanwhile, we would\nlike to combine this model with the topic-conditioned framework [10] as well as incorpo-\nrate hierarchical mixture model so that novelty detection will be conditioned on some topic,\nwhich will be modeled by either supervised or semi-supervised learning techniques.\n\n\nReferences\n\n[1]    The    2002    topic    detection    &    tracking    task    definition    and    evaluation    plan.\nhttp://www.nist.gov/speech/tests/tdt/tdt2002/evalplan.htm, 2002.\n\n[2] Allan, J., Lavrenko, V. & Jin, H. First story detection in tdt is hard. In Proc. of CIKM 2000.\n\n[3] Blei, D., Griffiths, T., Jordan, M. & Tenenbaum, J. Hierarchical topic models and the nested\nchinese restaurant process. Advances in Neural Information Processing Systems, 15, 2003.\n\n[4] Ferguson, T. A Bayesian analysis of some nonparametric problems. Annals of Statistics, 1:209\n230, 1973.\n\n[5] Gelman A., Carlin, J., Stern, H. & Rubin, D. Bayesian Data Analysis (2nd ed.). CHAPMAN &\nHALL/CRC, 2003.\n\n[6] Miller, D., Leek, T. & Schwartz, R. Bbn at trec 7: Using hidden markov models for information\nretrieval. In TREC-7, 1999.\n\n[7] Minka, T. A family of algorithms for approximate Bayesian inference. Ph.D. thesis, MIT, 2001.\n\n[8] West, M., Mueller, P. & Escobar, M.D. Hierarchical priors and mixture models, with application\nin regression and density estimation. In Aspects of Uncertainty: A tribute to D. V. Lindley, A.F.M.\nSmith and P. Freeman, (eds.), Wiley, New York.\n\n[9] Yang, Y., Pierce, T. & Carbonell, J. A Study on Retrospective and On-line Event Detection. In\nProc. of SIGIR 1998.\n\n[10] Yang, Y., Zhang, J., Carnobell, J. & Jin, C. Topic-conditioned novelty detection. In Proc. of 8th\nACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2002.\n\n[11] Zaragoza, H., Hiemstra, D., Tipping, D. & Robertson, S. Bayesian extension to the language\nmodel for ad hoc information retrieval. In Proc. SIGIR 2003.\n\n\f\n", "award": [], "sourceid": 2639, "authors": [{"given_name": "Jian", "family_name": "Zhang", "institution": null}, {"given_name": "Zoubin", "family_name": "Ghahramani", "institution": null}, {"given_name": "Yiming", "family_name": "Yang", "institution": null}]}