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### Investigating the Risks Associated With COVID-19 Using Topic Modeling

"The better we can track the virus, the better we can fight it." Since the outbreak of the novel coronavirus (COVID-19), it has become a significant and urgent threat to global health. Within months of the outbreak, thousands of research papers relating to its effects, risks and treatments have been published. The pace at which research is carried out is increasing at a fast rate. But it brings with it a new problem for someone wanting to look for answers.

### Exact marginal inference in Latent Dirichlet Allocation

Assume we have potential "causes" $z\in Z$, which produce "events" $w$ with known probabilities $\beta(w|z)$. We observe $w_1,w_2,...,w_n$, what can we say about the distribution of the causes? A Bayesian estimate will assume a prior on distributions on $Z$ (we assume a Dirichlet prior) and calculate a posterior. An average over that posterior then gives a distribution on $Z$, which estimates how much each cause $z$ contributed to our observations. This is the setting of Latent Dirichlet Allocation, which can be applied e.g. to topics "producing" words in a document. In this setting usually the number of observed words is large, but the number of potential topics is small. We are here interested in applications with many potential "causes" (e.g. locations on the globe), but only a few observations. We show that the exact Bayesian estimate can be computed in linear time (and constant space) in $|Z|$ for a given upper bound on $n$ with a surprisingly simple formula. We generalize this algorithm to the case of sparse probabilities $\beta(w|z)$, in which we only need to assume that the tree width of an "interaction graph" on the observations is limited. On the other hand we also show that without such limitation the problem is NP-hard.

### Automatic Identification of Types of Alterations in Historical Manuscripts

Alterations in historical manuscripts such as letters represent a promising field of research. On the one hand, they help understand the construction of text. On the other hand, topics that are being considered sensitive at the time of the manuscript gain coherence and contextuality when taking alterations into account, especially in the case of deletions. The analysis of alterations in manuscripts, though, is a traditionally very tedious work. In this paper, we present a machine learning-based approach to help categorize alterations in documents. In particular, we present a new probabilistic model (Alteration Latent Dirichlet Allocation, alterLDA in the following) that categorizes content-related alterations. The method proposed here is developed based on experiments carried out on the digital scholarly edition Berlin Intellectuals, for which alterLDA achieves high performance in the recognition of alterations on labelled data. On unlabelled data, applying alterLDA leads to interesting new insights into the alteration behavior of authors, editors and other manuscript contributors, as well as insights into sensitive topics in the correspondence of Berlin intellectuals around 1800. In addition to the findings based on the digital scholarly edition Berlin Intellectuals, we present a general framework for the analysis of text genesis that can be used in the context of other digital resources representing document variants. To that end, we present in detail the methodological steps that are to be followed in order to achieve such results, giving thereby a prime example of an Machine Learning application the Digital Humanities.

### Discriminative Topic Modeling with Logistic LDA

Despite many years of research into latent Dirichlet allocation (LDA), applying LDA to collections of non-categorical items is still challenging for practitioners. Yet many problems with much richer data share a similar structure and could benefit from the vast literature on LDA. We propose logistic LDA, a novel discriminative variant of latent Dirichlet allocation which is easy to apply to arbitrary inputs. In particular, our model can easily be applied to groups of images, arbitrary text embeddings, or integrate deep neural networks. Although it is a discriminative model, we show that logistic LDA can learn from unlabeled data in an unsupervised manner by exploiting the group structure present in the data.

### Gaussian Hierarchical Latent Dirichlet Allocation: Bringing Polysemy Back

Topic models are widely used to discover the latent representation of a set of documents. The two canonical models are latent Dirichlet allocation, and Gaussian latent Dirichlet allocation, where the former uses multinomial distributions over words, and the latter uses multivariate Gaussian distributions over pre-trained word embedding vectors as the latent topic representations, respectively. Compared with latent Dirichlet allocation, Gaussian latent Dirichlet allocation is limited in the sense that it does not capture the polysemy of a word such as bank.'' In this paper, we show that Gaussian latent Dirichlet allocation could recover the ability to capture polysemy by introducing a hierarchical structure in the set of topics that the model can use to represent a given document. Our Gaussian hierarchical latent Dirichlet allocation significantly improves polysemy detection compared with Gaussian-based models and provides more parsimonious topic representations compared with hierarchical latent Dirichlet allocation. Our extensive quantitative experiments show that our model also achieves better topic coherence and held-out document predictive accuracy over a wide range of corpus and word embedding vectors.

### Spatial Latent Dirichlet Allocation

In recent years, the language model Latent Dirichlet Allocation (LDA), which clusters co-occurring words into topics, has been widely appled in the computer vision field. However, many of these applications have difficulty with modeling the spatial and temporal structure among visual words, since LDA assumes that a document is a bag-of-words''. It is also critical to properly design words'' and "documents" when using a language model to solve vision problems. In this paper, we propose a topic model Spatial Latent Dirichlet Allocation (SLDA), which better encodes spatial structure among visual words that are essential for solving many vision problems. The spatial information is not encoded in the value of visual words but in the design of documents.

### Parallel Inference for Latent Dirichlet Allocation on Graphics Processing Units

The recent emergence of Graphics Processing Units (GPUs) as general-purpose parallel computing devices provides us with new opportunities to develop scalable learning methods for massive data. In this work, we consider the problem of parallelizing two inference methods on GPUs for latent Dirichlet Allocation (LDA) models, collapsed Gibbs sampling (CGS) and collapsed variational Bayesian (CVB). To address limited memory constraints on GPUs, we propose a novel data partitioning scheme that effectively reduces the memory cost. Furthermore, the partitioning scheme balances the computational cost on each multiprocessor and enables us to easily avoid memory access conflicts. We also use data streaming to handle extremely large datasets.

### Word Features for Latent Dirichlet Allocation

We extend Latent Dirichlet Allocation (LDA) by explicitly allowing for the encoding of side information in the distribution over words. This results in a variety of new capabilities, such as improved estimates for infrequently occurring words, as well as the ability to leverage thesauri and dictionaries in order to boost topic cohesion within and across languages. We present experiments on multi-language topic synchronisation where dictionary information is used to bias corresponding words towards similar topics. Results indicate that our model substantially improves topic cohesion when compared to the standard LDA model. Papers published at the Neural Information Processing Systems Conference.

### Relative Performance Guarantees for Approximate Inference in Latent Dirichlet Allocation

Hierarchical probabilistic modeling of discrete data has emerged as a powerful tool for text analysis. Posterior inference in such models is intractable, and practitioners rely on approximate posterior inference methods such as variational inference or Gibbs sampling. There has been much research in designing better approximations, but there is yet little theoretical understanding of which of the available techniques are appropriate, and in which data analysis settings. In this paper we provide the beginnings of such understanding. We analyze the improvement that the recently proposed collapsed variational inference (CVB) provides over mean field variational inference (VB) in latent Dirichlet allocation.

### Online Learning for Latent Dirichlet Allocation

We develop an online variational Bayes (VB) algorithm for Latent Dirichlet Allocation (LDA). Online LDA is based on online stochastic optimization with a natural gradient step, which we show converges to a local optimum of the VB objective function. It can handily analyze massive document collections, including those arriving in a stream. We study the performance of online LDA in several ways, including by fitting a 100-topic topic model to 3.3M articles from Wikipedia in a single pass. We demonstrate that online LDA finds topic models as good or better than those found with batch VB, and in a fraction of the time.