arXiv subjects

Páidí Creed

Publications and source records attributed to Páidí Creed.

4 recordsLinked to original sources

arXiv2022

Contrastive Mixture of Posteriors for Counterfactual Inference, Data Integration and Fairness

Learning meaningful representations of data that can address challenges such as batch effect correction and counterfactual inference is a central problem in many domains including computational biology. Adopting a Conditional VAE framework, we show that marginal independence between the representation and a condition variable plays a key role in both of these challenges. We propose the Contrastive Mixture of Posteriors (CoMP) method that uses a novel misalignment penalty defined in terms of mixtures of the variational posteriors to enforce this independence in latent space. We show that CoMP has attractive theoretical properties compared to previous approaches, and we prove counterfactual identifiability of CoMP under additional assumptions. We demonstrate state-of-the-art performance on a set of challenging tasks including aligning human tumour samples with cancer cell-lines, predicting transcriptome-level perturbation responses, and batch correction on single-cell RNA sequencing data. We also find parallels to fair representation learning and demonstrate that CoMP is competitive on a common task in the field.

stat.ML↗

arXiv2021

Directed Graph Embeddings in Pseudo-Riemannian Manifolds

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.

stat.ML↗

arXiv2014

The tractability of CSP classes defined by forbidden patterns

The constraint satisfaction problem (CSP) is a general problem central to computer science and artificial intelligence. Although the CSP is NP-hard in general, considerable effort has been spent on identifying tractable subclasses. The main two approaches consider structural properties (restrictions on the hypergraph of constraint scopes) and relational properties (restrictions on the language of constraint relations). Recently, some authors have considered hybrid properties that restrict the constraint hypergraph and the relations simultaneously. Our key contribution is the novel concept of a CSP pattern and classes of problems defined by forbidden patterns (which can be viewed as forbidding generic subproblems). We describe the theoretical framework which can be used to reason about classes of problems defined by forbidden patterns. We show that this framework generalises relational properties and allows us to capture known hybrid tractable classes. Although we are not close to obtaining a dichotomy concerning the tractability of general forbidden patterns, we are able to make some progress in a special case: classes of problems that arise when we can only forbid binary negative patterns (generic subproblems in which only inconsistent tuples are specified). In this case we are able to characterise very large classes of tractable and NP-hard forbidden patterns. This leaves the complexity of just one case unresolved and we conjecture that this last case is tractable.

cs.AI↗

arXiv2012

The number of Euler tours of a random directed graph

In this paper we obtain the expectation and variance of the number of Euler tours of a random Eulerian directed graph with fixed out-degree sequence. We use this to obtain the asymptotic distribution of the number of Euler tours of a random $d$-in/$d$-out graph and prove a concentration result. We are then able to show that a very simple approach for uniform sampling or approximately counting Euler tours yields algorithms running in expected polynomial time for almost every $d$-in/$d$-out graph. We make use of the BEST theorem of de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte, which shows that the number of Euler tours of an Eulerian directed graph with out-degree sequence $\mathbf{d}$ is the product of the number of arborescences and the term $\frac{1}{n}[\prod_{v \in V}(d_v-1)!]$. Therefore most of our effort is towards estimating the moments of the number of arborescences of a random graph with fixed out-degree sequence.

cs.DM↗