Differentiable Learning of Sequence-Specific Minimizer Schemes with DeepMinimizer

Abstract

Minimizers are widely used to sample representative k -mers from biological sequences in many applications, such as read mapping and taxonomy prediction. In most scenarios, having the minimizer scheme select as few k -mer positions as possible (i.e., having a low density) is desirable to reduce computation and memory cost. Despite the growing interest in minimizers, learning an effective scheme with optimal density is still an open question, as it requires solving an apparently challenging discrete optimization problem on the permutation space of k -mer orderings. Most existing schemes are designed to work well in expectation over random sequences, which have limited applicability to many practical tools. On the other hand, several methods have been proposed to construct minimizer schemes for a specific target sequence. These methods, however, only approximate the original objective with likewise discrete surrogate tasks that are not able to significantly improve the density performance. This article introduces the first continuous relaxation of the density minimizing objective, DeepMinimizer , which employs a novel Deep Learning twin architecture to simultaneously ensure both validity and performance of the minimizer scheme. Our surrogate objective is fully differentiable and, therefore, amenable to efficient gradient-based optimization using GPU computing. Finally, we demonstrate that DeepMinimizer discovers minimizer schemes that significantly outperform state-of-the-art constructions on human genomic sequences.

Efficient minimizer orders for large values ofkusing minimum decycling sets

“…The density factor normalizes density for the window size w of the scheme. We follow the definition of Zheng et al [8]: for a sequence S the density factor is df (S) = factor removes the dependence on L, e.g. making the expected density factor of all random minimizers the same, regardless of k and L. Note that other works define the density factor simply as the density times a factor of (w +1) (c.f.…”

Masked Minimizers: Unifying sequence sketching methods

“…The sampling function of a minimizer scheme is characterized by a tuple of parameters ( w, k, π ), where w and k are defined above. Additionally, π is a total ordering over the set of all k -mers, which can be represented [7] as a scoring function , such that for every pair of k -mers k, κ′ ∈ Σ k : …”

“…Varying the mask configuration induces a spectrum of comparable schemes, including minimizers (i.e., all-ones mask) and various syncmer schemes (i.e., one-hot masks). This unification reveals a methodical approach to derive comparable sketching schemes via combining existing minimizer construction/optimization techniques [7, 5, 21, 22] with a mask optimization routine.…”

“…We propose a sequence-specific learning objective to optimize the masked minimizer scheme with respect to the GSS metric. Our objective function extends the D eep M inimizer loss function [7] with a secondary objective that minimizes the expected change in local ordering of k -mers under random mutations. Our approach consistently improves the GSS metric for every mask variant and outperform other known minimizer optimization approaches such as M iniception [21], PASHA [5] and D eep M inimizer [7].…”

“…Our objective function extends the D eep M inimizer loss function [7] with a secondary objective that minimizes the expected change in local ordering of k -mers under random mutations. Our approach consistently improves the GSS metric for every mask variant and outperform other known minimizer optimization approaches such as M iniception [21], PASHA [5] and D eep M inimizer [7]. We further conduct ablation studies to reveal practical insights about masked minimizers, such as the existence of trivial solutions, mask performance profiles and the ability to safeguard against a common minimizer pitfall.…”