The continued scaling of genetic perturbation technologies combined with high-dimensional assays such as cellular microscopy and RNA-sequencing has enabled genome-scale reverse-genetics experiments that go beyond single-endpoint measurements of growth or lethality. Datasets emerging from these experiments can be combined to construct perturbative "maps of biology", in which readouts from various manipulations (e.g., CRISPR-Cas9 knockout, CRISPRi knockdown, compound treatment) are placed in unified, relatable embedding spaces allowing for the generation of genome-scale sets of pairwise comparisons. These maps of biology capture known biological relationships and uncover new associations which can be used for downstream discovery tasks. Construction of these maps involves many technical choices in both experimental and computational protocols, motivating the design of benchmark procedures to evaluate map quality in a systematic, unbiased manner. Here, we (1) establish a standardized terminology for the steps involved in perturbative map building, (2) introduce key classes of benchmarks to assess the quality of such maps, (3) construct 18 maps from four genome-scale datasets employing different cell types, perturbation technologies, and data readout modalities, (4) generate benchmark metrics for the constructed maps and investigate the reasons for performance variations, and (5) demonstrate utility of these maps to discover new biology by suggesting roles for two largely uncharacterized genes.

Physics-informed neural networks (PINNs) are emerging as popular mesh-free solvers for partial differential equations (PDEs). Recent extensions decompose the domain, apply different PINNs to solve the problem in each subdomain, and stitch the subdomains at the interface. Thereby, they can further alleviate the problem complexity, reduce the computational cost, and allow parallelization. However, the performance of multi-domain PINNs is sensitive to the choice of the interface conditions. While quite a few conditions have been proposed, there is no suggestion about how to select the conditions according to specific problems. To address this gap, we propose META Learning of Interface Conditions (METALIC), a simple, efficient yet powerful approach to dynamically determine appropriate interface conditions for solving a family of parametric PDEs. Specifically, we develop two contextual multi-arm bandit (MAB) models. The first one applies to the entire training course, and online updates a Gaussian process (GP) reward that given the PDE parameters and interface conditions predicts the performance. We prove a sub-linear regret bound for both UCB and Thompson sampling, which in theory guarantees the effectiveness of our MAB. The second one partitions the training into two stages, one is the stochastic phase and the other deterministic phase; we update a GP reward for each phase to enable different condition selections at the two stages to further bolster the flexibility and performance. We have shown the advantage of METALIC on four bench-mark PDE families.

We propose a nonparametric factorization approach for sparsely observed tensors. The sparsity does not mean zero-valued entries are massive or dominated. Rather, it implies the observed entries are very few, and even fewer with the growth of the tensor; this is ubiquitous in practice. Compared with the existent works, our model not only leverages the structural information underlying the observed entry indices, but also provides extra interpretability and flexibility {—} it can simultaneously estimate a set of location factors about the intrinsic properties of the tensor nodes, and another set of sociability factors reflecting their extrovert activity in interacting with others; users are free to choose a trade-off between the two types of factors. Specifically, we use hierarchical Gamma processes and Poisson random measures to construct a tensor-valued process, which can freely sample the two types of factors to generate tensors and always guarantees an asymptotic sparsity. We then normalize the tensor process to obtain hierarchical Dirichlet processes to sample each observed entry index, and use a Gaussian process to sample the entry value as a nonlinear function of the factors, so as to capture both the sparse structure properties and complex node relationships. For efficient inference, we use Dirichlet process properties over finite sample partitions, density transformations, and random features to develop a stochastic variational estimation algorithm. We demonstrate the advantage of our method in several benchmark datasets.

High-order interaction events are common in real-world applications. Learning embeddings that encode the complex relationships of the participants from these events is of great importance in knowledge mining and predictive tasks. Despite the success of existing approaches, e.g. Poisson tensor factorization, they ignore the sparse structure underlying the data, namely the occurred interactions are far less than the possible interactions among all the participants. In this paper, we propose Nonparametric Embeddings of Sparse High-order interaction events (NESH). We hybridize a sparse hypergraph (tensor) process and a matrix Gaussian process to capture both the asymptotic structural sparsity within the interactions and nonlinear temporal relationships between the participants. We prove strong asymptotic bounds (including both a lower and an upper bound ) of the sparse ratio, which reveals the asymptotic properties of the sampled structure. We use batch-normalization, stick-breaking construction and sparse variational GP approximations to develop an efficient, scalable model inference algorithm. We demonstrate the advantage of our approach in several real-world applications.

Tensor decomposition is a powerful framework for multiway data analysis. Despite the success of existing approaches, they ignore the sparse nature of the tensor data in many real-world applications, explicitly or implicitly assuming dense tensors. To address this model misspecification and to exploit the sparse tensor structures, we propose Nonparametric dEcomposition of Sparse Tensors (\ours), which can capture both the sparse structure properties and complex relationships between the tensor nodes to enhance the embedding estimation. Specifically, we first use completely random measures to construct tensor-valued random processes. We prove that the entry growth is much slower than that of the corresponding tensor size, which implies sparsity. Given finite observations (\ie projections), we then propose two nonparametric decomposition models that couple Dirichlet processes and Gaussian processes to jointly sample the sparse entry indices and the entry values (the latter as a nonlinear mapping of the embeddings), so as to encode both the structure properties and nonlinear relationships of the tensor nodes into the embeddings. Finally, we use the stick-breaking construction and random Fourier features to develop a scalable, stochastic variational learning algorithm. We show the advantage of our approach in sparse tensor generation, and entry index and value prediction in several real-world applications.

Tensor decomposition is a fundamental framework to model and analyze multiway data, which are ubiquitous in realworld applications. A critical challenge of tensor decomposition is to capture a variety of complex relationships/interactions while avoiding overfitting the data that are usually very sparse. Although numerous tensor decomposition methods have been proposed, they are mostly based on a multilinear form and hence are incapable of estimating more complex, nonlinear relationships. To address the challenge, we propose POND, PrObabilistic Neural-kernel tensor Decomposition that unifies the self-adaptation of Bayes nonparametric function learning and the expressive power of neural networks. POND uses Gaussian processes (GPs) to model the hidden relationships and can automatically detect their complexity in tensors, preventing both underfitting and overfitting. POND then incorporates convolutional neural networks to construct the GP kernel to greatly promote the capability of estimating highly nonlinear relationships. To scale POND to large data, we use the sparse variational GP framework and reparameterization trick to develop an efficient stochastic variational learning algorithm. On both synthetic and real-world benchmark datasets, POND often exhibits better predictive performance than the state-of-the-art nonlinear tensor decomposition methods. In addition, as a Bayesian approach, POND provides the posterior distribution of the latent factors, and hence can conveniently quantify their uncertainty and the confidence levels for predictions.