Jonathan Warrell

Francesco Alesiani, Jonathan Warrell, Tanja Bien et al.

We propose LOGDIFF (Logical Guidance for the Exact Composition of Diffusion Models), a guidance framework for diffusion models that enables principled constrained generation with complex logical expressions at inference time. We study when exact score-based guidance for complex logical formulas can be obtained from guidance signals associated with atomic properties. First, we derive an exact Boolean calculus that provides a sufficient condition for exact logical guidance. Specifically, if a formula admits a circuit representation in which conjunctions combine conditionally independent subformulas and disjunctions combine subformulas that are either conditionally independent or mutually exclusive, exact logical guidance is achievable. In this case, the guidance signal can be computed exactly from atomic scores and posterior probabilities using an efficient recursive algorithm. Moreover, we show that, for commonly encountered classes of distributions, any desired Boolean formula is compilable into such a circuit representation. Second, by combining atomic guidance scores with posterior probability estimates, we introduce a hybrid guidance approach that bridges classifierguidance and classifier-free guidance, applicable to both compositional logical guidance and standard conditional generation. We demonstrate the effectiveness of our framework on multiple image and protein structure generation tasks.

Jonathan Warrell, Mark Gerstein

Deep Probabilistic Programming (DPP) allows powerful models based on recursive computation to be learned using efficient deep-learning optimization techniques. Additionally, DPP offers a unified perspective, where inference and learning algorithms are treated on a par with models as stochastic programs. Here, we offer a framework for representing and learning flexible PAC-Bayes bounds as stochastic programs using DPP-based methods. In particular, we show that DPP techniques may be leveraged to derive generalization bounds that draw on the compositionality of DPP representations. In turn, the bounds we introduce offer principled training objectives for higher-order probabilistic programs. We offer a definition of a higher-order generalization bound, which naturally encompasses single- and multi-task generalization perspectives (including transfer- and meta-learning) and a novel class of bound based on a learned measure of model complexity. Further, we show how modified forms of all higher-order bounds can be efficiently optimized as objectives for DPP training, using variational techniques. We test our framework using single- and multi-task generalization settings on synthetic and biological data, showing improved performance and generalization prediction using flexible DPP model representations and learned complexity measures.

Jonathan Warrell, Alexey Potapov, Adam Vandervorst et al.

We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge (programs/proofs), but also appropriate ways of reasoning (logics/type systems). We draw on the frameworks of cubical type theory and dependent typed metagraphs to formalize our approach. In doing so, we show that specific constructions within the meta-language can be related via bisimulation (implying path equivalence) to the type systems they correspond. This allows our approach to provide a convenient means of deriving synthetic denotational semantics for various type systems. Particularly, we derive bisimulations for pure type systems (PTS), and probabilistic dependent type systems (PDTS). We discuss further the relationship of PTS to non-well-founded set theory, and demonstrate the feasibility of our approach with an implementation of a bisimulation proof in a Guarded Cubical Type Theory type checker.

Jonathan Warrell, Hussein Mohsen, Mark Gerstein

A variety of methods have been proposed for interpreting nodes in deep neural networks, which typically involve scoring nodes at lower layers with respect to their effects on the output of higher-layer nodes (where lower and higher layers are closer to the input and output layers, respectively). However, we may be interested in picking out a prioritized collection of subsets of the inputs across a range of scales according to their importance for an output node, and not simply a prioritized ranking across the inputs as singletons. Such a situation may arise in biological applications, for instance, where we are interested in epistatic effects between groups of genes in determining a trait of interest. Here, we outline a flexible framework which may be used to generate multiscale network interpretations, using any previously defined scoring function. We demonstrate the ability of our method to pick out biologically important genes and gene sets in the domains of cancer and psychiatric genomics.

Jonathan H. Warrell, Musa M. Mhlanga

Coregulation of the expression of groups of genes has been extensively demonstrated empirically in bacterial and eukaryotic systems. Such coregulation can arise through the use of shared regulatory motifs, which allow the coordinated expression of modules (and module groups) of functionally related genes across the genome. Coregulation can also arise through the physical association of multi-gene complexes through chromosomal looping, which are then transcribed together. We present a general formalism for modeling coregulation rules in the framework of Random Boolean Networks (RBN), and develop specific models for transcription factor networks with modular structure (including module groups, and multi-input modules (MIM) with autoregulation) and multi-gene complexes (including hierarchical differentiation between multi-gene complex members). We develop a mean-field approach to analyse the stability of large networks incorporating coregulation, and show that autoregulated MIM and hierarchical gene-complex models can achieve greater stability than networks without coregulation whose rules have matching activation frequency. We provide further analysis of the stability of small networks of both kinds through simulations. We also characterize several general properties of the transients and attractors in the hierarchical coregulation model, and show using simulations that the steady-state distribution factorizes hierarchically as a Bayesian network in a Markov Jump Process analogue of the RBN model.

Jonathan H. Warrell, Anca F. Savulescu, Robyn Brackin et al.

We derive generalized estimators for a number of spatial statistics that have been used in the analysis of spatially resolved omics data, such as Ripley's K, H and L functions, clustering index, and degree of clustering, which allow these statistics to be calculated on data modelled by arbitrary random measures (RMs). Our estimators generalize those typically used to calculate these statistics on point process data, allowing them to be calculated on RMs which assign continuous values to spatial regions, for instance to model protein intensity. The clustering index (H*) compares Ripley's H function calculated empirically to its distribution under complete spatial randomness (CSR), leading us to consider CSR null hypotheses for RMs which are not point-processes when generalizing this statistic. We thus consider restricted classes of completely random measures which can be simulated directly (Gamma processes and Marked Poisson Processes), as well as the general class of all CSR RMs, for which we derive an exact permutation-based H* estimator. We establish several properties of the estimators, including bounds on the accuracy of our general Ripley K estimator, its relationship to a previous estimator for the cross-correlation measure, and the relationship of our generalized H* estimator to previous statistics. To test the ability of our approach to identify spatial patterning, we use Fluorescent In Situ Hybridization (FISH) and Immunofluorescence (IF) data to probe for mRNA and protein subcellular localization patterns respectively in polarizing mouse fibroblasts on micropattened cells. We observe correlated patterns of clustering over time for corresponding mRNAs and proteins, suggesting a deterministic effect of mRNA localization on protein localization for several pairs tested, including one case in which spatial patterning at the mRNA level has not been previously demonstrated.

Vibhav Vineet, Jonathan Warrell, Philip H. S. Torr

A large number of problems in computer vision can be modelled as energy minimization problems in a Markov Random Field (MRF) or Conditional Random Field (CRF) framework. Graph-cuts based $α$-expansion is a standard move-making method to minimize the energy functions with sub-modular pairwise terms. However, certain problems require more complex pairwise terms where the $α$-expansion method is generally not applicable. In this paper, we propose an iterative {\em tiered move making algorithm} which is able to handle general pairwise terms. Each move to the next configuration is based on the current labeling and an optimal tiered move, where each tiered move requires one application of the dynamic programming based tiered labeling method introduced in Felzenszwalb et. al. \cite{tiered_cvpr_felzenszwalbV10}. The algorithm converges to a local minimum for any general pairwise potential, and we give a theoretical analysis of the properties of the algorithm, characterizing the situations in which we can expect good performance. We first evaluate our method on an object-class segmentation problem using the Pascal VOC-11 segmentation dataset where we learn general pairwise terms. Further we evaluate the algorithm on many other benchmark labeling problems such as stereo, image segmentation, image stitching and image denoising. Our method consistently gets better accuracy and energy values than alpha-expansion, loopy belief propagation (LBP), quadratic pseudo-boolean optimization (QPBO), and is competitive with TRWS.

Ming-Ming Cheng, Shuai Zheng, Wen-Yan Lin et al.

Humans describe images in terms of nouns and adjectives while algorithms operate on images represented as sets of pixels. Bridging this gap between how humans would like to access images versus their typical representation is the goal of image parsing, which involves assigning object and attribute labels to pixel. In this paper we propose treating nouns as object labels and adjectives as visual attribute labels. This allows us to formulate the image parsing problem as one of jointly estimating per-pixel object and attribute labels from a set of training images. We propose an efficient (interactive time) solution. Using the extracted labels as handles, our system empowers a user to verbally refine the results. This enables hands-free parsing of an image into pixel-wise object/attribute labels that correspond to human semantics. Verbally selecting objects of interests enables a novel and natural interaction modality that can possibly be used to interact with new generation devices (e.g. smart phones, Google Glass, living room devices). We demonstrate our system on a large number of real-world images with varying complexity. To help understand the tradeoffs compared to traditional mouse based interactions, results are reported for both a large scale quantitative evaluation and a user study.