If you are dealing with Statistics, Data Science, Machine Learning, Artificial Intelligence or even general Computer Science, Mathematics, Engineering or Physics, you've probably come across the term Entropy more than once. Entropy is a significant, widely used and above all successful measure for quantifying inhomogeneity, impurity, complexity and uncertainty or unpredictability. The concept of entropy is more than 200 years old, and still, or perhaps because of that, it is an integral part of the latest machine learning models that are successfully deployed on real-world data sets. In this article, I want to highlight the simplicity, beauty and meaning of entropy. Entropy and its special forms are able to achieve a conceptual understanding of the data in an intuitive way--something we should exploit more often.

We propose a topological learning algorithm for the estimation of the conditional dependency structure of large sets of random variables from sparse and noisy data. The algorithm, named Maximally Filtered Clique Forest (MFCF), produces a clique forest and an associated Markov Random Field (MRF) by generalising Prim's minimum spanning tree algorithm. To the best of our knowledge, the MFCF presents three elements of novelty with respect to existing structure learning approaches. The first is the repeated application of a local topological move, the clique expansion, that preserves the decomposability of the underlying graph. Through this move the decomposability and calculation of scores is performed incrementally at the variable (rather than edge) level, and this provides better computational performance and an intuitive application of multivariate statistical tests. The second is the capability to accommodate a variety of score functions and, while this paper is focused on multivariate normal distributions, it can be directly generalised to different types of statistics. Finally, the third is the variable range of allowed clique sizes which is an adjustable topological constraint that acts as a topological penalizer providing a way to tackle sparsity at $l_0$ semi-norm level; this allows a clean decoupling of structure learning and parameter estimation. The MFCF produces a representation of the clique forest, together with a perfect ordering of the cliques and a perfect elimination ordering for the vertices. As an example we propose an application to covariance selection models and we show that the MCFC outperforms the Graphical Lasso for a number of classes of matrices.

Spatial studies of transcriptome provide biologists with gene expression maps of heterogeneous and complex tissues. However, most experimental protocols for spatial transcriptomics suffer from the need to select beforehand a small fraction of genes to be quantified over the entire transcriptome. Standard single-cell RNA sequencing (scRNA-seq) is more prevalent, easier to implement and can in principle capture any gene but cannot recover the spatial location of the cells. In this manuscript, we focus on the problem of imputation of missing genes in spatial transcriptomic data based on (unpaired) standard scRNA-seq data from the same biological tissue. Building upon domain adaptation work, we propose gimVI, a deep generative model for the integration of spatial transcriptomic data and scRNA-seq data that can be used to impute missing genes. After describing our generative model and an inference procedure for it, we compare gimVI to alternative methods from computational biology or domain adaptation on real datasets and outperform Seurat Anchors, Liger and CORAL to impute held-out genes.

There is an abundance of complex dynamic systems that are critical to our daily lives and our society but that are hardly understood, and even with today's possibilities to sense and collect large amounts of experimental data, they are so complex and continuously evolving that it is unlikely that their dynamics will ever be understood in full detail. Nevertheless, through computational tools we can try to make the best possible use of the current technologies and available data. We believe that the most useful models will have to take into account the imbalance between system complexity and available data in the context of limited knowledge or multiple hypotheses. The complex system of biological cells is a prime example of such a system that is studied in systems biology and has motivated the methods presented in this paper. They were developed as part of the DARPA Rapid Threat Assessment (RTA) program, which is concerned with understanding of the mechanism of action (MoA) of toxins or drugs affecting human cells. Using a combination of Gaussian processes and abstract network modeling, we present three fundamentally different machine-learning-based approaches to learn causal relations and synthesize causal networks from high-dimensional time series data. While other types of data are available and have been analyzed and integrated in our RTA work, we focus on transcriptomics (that is gene expression) data obtained from high-throughput microarray experiments in this paper to illustrate capabilities and limitations of our algorithms. Our algorithms make different but overall relatively few biological assumptions, so that they are applicable to other types of biological data and potentially even to other complex systems that exhibit high dimensionality but are not of biological nature.

Domain adaptation provides a powerful set of model training techniques given domain-specific training data and supplemental data with unknown relevance. The techniques are useful when users need to develop models with data from varying sources, of varying quality, or from different time ranges. We build CrossTrainer, a system for practical domain adaptation. CrossTrainer utilizes loss reweighting, which provides consistently high model accuracy across a variety of datasets in our empirical analysis. However, loss reweighting is sensitive to the choice of a weight hyperparameter that is expensive to tune. We develop optimizations leveraging unique properties of loss reweighting that allow CrossTrainer to output accurate models while improving training time compared to naive hyperparameter search.

High-level synthesis (HLS) shortens the development time of hardware designs and enables faster design space exploration at a higher abstraction level. Optimization of complex applications in HLS is challenging due to the effects of implementation issues such as routing congestion. Routing congestion estimation is absent or inaccurate in existing HLS design methods and tools. Early and accurate congestion estimation is of great benefit to guide the optimization in HLS and improve the efficiency of implementation. However, routability, a serious concern in FPGA designs, has been difficult to evaluate in HLS without analyzing post-implementation details after Place and Route. To this end, we propose a novel method to predict routing congestion in HLS using machine learning and map the expected congested regions in the design to the relevant high-level source code. This is greatly beneficial in early identification of routability oriented bottlenecks in the high-level source code without running time-consuming register-transfer level (RTL) implementation flow. Experiments demonstrate that our approach accurately estimates vertical and horizontal routing congestion with errors of 6.71% and 10.05% respectively. By presenting Face Detection application as a case study, we show that by discovering the bottlenecks in high-level source code, routing congestion can be easily and quickly resolved compared to the efforts involved in RTL implementation and design feedback.

The pervasive brittleness of deep neural networks [Sze 14; Eng 19; HD19; Ath 18] has attracted significant attention in recent years. Particularly worrisome is the phenomenon of adversarial examples [Big 13; Sze 14], imperceptibly perturbed natural inputs that induce erroneous predictions in state-of-the-art classifiers. Previous work has proposed a variety of explanations for this phenomenon, ranging from theoretical models [Sch 18; BPR18] to arguments based on concentration of measure in high-dimensions [Gil 18; MDM18; Sha 19a]. These theories, however, are often unable to fully capture behaviors we observe in practice (we discuss this further in Section 5). More broadly, previous work in the field tends to view adversarial examples as aberrations arising either from the high dimensional nature of the input space or statistical fluctuations in the training data [Sze 14; GSS15; Gil 18]. From this point of view, it is natural to treat adversarial robustness as a goal that can be disentangled and pursued independently from maximizing accuracy [Mad 18; SHS19; Sug 19], either through improved standard regularization methods [TG16] or pre/post-processing of network inputs/outputs [Ues 18; CW17a; He 17].

There is a growing need for fast and accurate methods for testing developmental neurotoxicity across several chemical exposure sources. Current approaches, such as in vivo animal studies, and assays of animal and human primary cell cultures, suffer from challenges related to time, cost, and applicability to human physiology. We previously demonstrated success employing machine learning to predict developmental neurotoxicity using gene expression data collected from human 3D tissue models exposed to various compounds. The 3D model is biologically similar to developing neural structures, but its complexity necessitates extensive expertise and effort to employ. By instead focusing solely on constructing an assay of developmental neurotoxicity, we propose that a simpler 2D tissue model may prove sufficient. We thus compare the accuracy of predictive models trained on data from a 2D tissue model with those trained on data from a 3D tissue model, and find the 2D model to be substantially more accurate. Furthermore, we find the 2D model to be more robust under stringent gene set selection, whereas the 3D model suffers substantial accuracy degradation. While both approaches have advantages and disadvantages, we propose that our described 2D approach could be a valuable tool for decision makers when prioritizing neurotoxicity screening.

The Unbiased Learning-to-Rank framework has been recently proposed as a general approach to systematically remove biases, such as position bias, from learning-to-rank models. The method takes two steps - estimating click propensities and using them to train unbiased models. Most common methods proposed in the literature for estimating propensities involve some degree of intervention in the live search engine. An alternative approach proposed recently uses an Expectation Maximization (EM) algorithm to estimate propensities by using ranking features for estimating relevances. In this work we propose a novel method to directly estimate propensities which does not use any intervention in live search or rely on modeling relevance. Rather, we take advantage of the fact that the same query-document pair may naturally change ranks over time. This typically occurs for eCommerce search because of change of popularity of items over time, existence of time dependent ranking features, or addition or removal of items to the index (an item getting sold or a new item being listed). However, our method is general and can be applied to any search engine for which the rank of the same document may naturally change over time for the same query. We derive a simple likelihood function that depends on propensities only, and by maximizing the likelihood we are able to get estimates of the propensities. We apply this method to eBay search data to estimate click propensities for web and mobile search and compare these with estimates using the EM method. We also use simulated data to show that the method gives reliable estimates of the "true" simulated propensities. Finally, we train an unbiased learning-to-rank model for eBay search using the estimated propensities and show that it outperforms both baselines - one without position bias correction and one with position bias correction using the EM method.

Gene interaction graphs aim to capture various relationships between genes and can be used to create more biologically-intuitive models for machine learning. There are many such graphs available which can differ in the number of genes and edges covered. In this work, we attempt to evaluate the biases provided by those graphs through utilizing them for 'Single Gene Inference' (SGI) which serves as, what we believe is, a proxy for more relevant prediction tasks. The SGI task assesses how well a gene's neighbors in a particular graph can 'explain' the gene itself in comparison to the baseline of using all the genes in the dataset. We evaluate seven major gene interaction graphs created by different research groups on two distinct datasets, TCGA and GTEx. We find that some graphs perform on par with the unbiased baseline for most genes with a significantly smaller feature set.