Correlation-compressed direct-coupling analysis

Abstract

Learning Ising or Potts models from data has become an important topic in statistical physics and computational biology, with applications to predictions of structural contacts in proteins and other areas of biological data analysis. The corresponding inference problems are challenging since the normalization constant (partition function) of the Ising/Potts distributions cannot be computed efficiently on large instances. Different ways to address this issue have hence given size to a substantial methodological literature. In this paper we investigate how these methods could be used on much larger datasets than studied previously. We focus on a central aspect, that in practice these inference problems are almost always severely under-sampled, and the operational result is almost always a small set of leading (largest) predictions. We therefore explore an approach where the data is pre-filtered based on empirical correlations, which can be computed directly even for very large problems. Inference is only used on the much smaller instance in a subsequent step of the analysis. We show that in several relevant model classes such a combined approach gives results of almost the same quality as the computationally much more demanding inference on the whole dataset. We also show that results on whole-genome epistatic couplings that were obtained in a recent computation-intensive study can be retrieved by the new approach. The method of this paper hence opens up the possibility to learn parameters describing pair-wise dependencies in whole genomes in a computationally feasible and expedient manner.ily related to spatial contacts [13,18,33].The actual use of DCA is comprised of two parts: (1) to run the inference procedure of choice on an MSA which consists of N samples, each of dimension L; and (2) to keep only a subset of largest predictions for further assessment and use. We will refer to the columns of the MSA as loci, the variables in each column as alleles, and the rows as samples. The MSA hence consists of N samples with each sample being a list of L alleles. Alternatively we will refer to L as the data dimension and N as the sample size. The total number of parameters in the inferred Ising or Potts models is proportional to L 2 and will here be denoted P. The number of retained predictions will be denoted K.Exact frequentist or Bayesian-point estimate methods, i.e. maximum likelihood (ML) or maximum a posteriori (MAP), are not computationally feasible for the data dimensions of current practical interest, and many approximate inference methods have therefore been developed [26]. Additionally statistical identifiability demands that K cannot be larger than N ; one cannot learn more features from the data than there are examples. This has indeed mostly been the case in the examples above. However, in the intermediate step P parameters are inferred, and in many (if not all) cases of interest P ∼ L 2 has been much larger than N . On top of inference being approximate it must therefore also be regularized.The setting whe...

Genome-wide epistasis and co-selection study using mutual information

“…In contrast to our method, however, Cui et al did not attempt to disentangle the direct interaction from the indirect interactions. In a recent hybrid approach, Gao et al proposed filtering the data based on pairwise correlations and then fitting a joint model over the remaining sites in ( 49 ). The obvious advantage of a strict pairwise method, such as SpydrPick, is that its computational simplicity allows for scaling up to data sets beyond what is currently achievable by current DCA-based methods.…”

adabmDCA: adaptive Boltzmann machine learning for biological sequences

“…set to zero) a subset of the parameters observing that even though large spurious correlations may arise from non topologically connected sites, weak correlations are typically associated with small coupling strengths. As explained in [22], one can first determine a starting topology and then run the learning procedure on it. To this end, adabmDCA provides two distinct strategies.…”

“…A practical way to control this behavior is to impose a sparsity prior over the coupling matrices: the two most used priors are the so called ℓ 1 and ℓ 2 regularizations, which force the inferred couplings to minimize the associated ℓ 1 and ℓ 2 norms multiplied by a tunable parameter that sets the regularization strength. A complementary approach consists in setting a priori a probable topology suggested by the mutual information between all pairs of residues [22]. Here, as discussed in the following section, we will follow an information-based decimation protocol originally proposed in [11].…”

Inference of compressed Potts graphical models

“…Moreover the reduction of computational time obtained thanks to color compression and sparsity is necessary when dealing with larger number of sites, e.g. whole genome inference [27,52]. Last of all, let us emphasize that the color compression/decompression procedure introduced here is not restricted to pairwise graphical models.…”