Franziska Biegler

Assessment and Validation of Machine Learning Methods for Predicting Molecular Atomization Energies

The accurate and reliable prediction of properties of molecules typically requires computationally intensive quantum-chemical calculations. Recently, machine learning techniques applied to ab initio calculations have been proposed as an efficient approach for describing the energies of molecules in their given ground-state structure throughout chemical compound space (Rupp et al. Phys. Rev. Lett. 2012, 108, 058301). In this paper we outline a number of established machine learning techniques and investigate the influence of the molecular representation on the methods performance. The best methods achieve prediction errors of 3 kcal/mol for the atomization energies of a wide variety of molecules. Rationales for this performance improvement are given together with pitfalls and challenges when applying machine learning approaches to the prediction of quantum-mechanical observables.

Machine Learning Predictions of Molecular Properties: Accurate Many-Body Potentials and Nonlocality in Chemical Space

Simultaneously accurate and efficient prediction of molecular properties throughout chemical compound space is a critical ingredient toward rational compound design in chemical and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to estimate atomization and total energies of molecules. These methods range from a simple sum over atoms, to addition of bond energies, to pairwise interatomic force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equilibrium molecular geometries, even simple pairwise force fields demonstrate prediction accuracy comparable to benchmark energies calculated using density functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the “holy grail” of chemical accuracy of 1 kcal/mol for both equilibrium and out-of-equilibrium geometries. This remarkable accuracy is achieved by a vectorized representation of molecules (so-called Bag of Bonds model) that exhibits strong nonlocality in chemical space. In addition, the same representation allows us to predict accurate electronic properties of molecules, such as their polarizability and molecular frontier orbital energies.

Regulated RNA rewriting: Modelling RNA editing with guided insertion

RNA editing is an important alternative genetic processing event that is known to take place in all higher eukaryotes. We study a model of string rewriting based on the sophisticated RNA editing mechanism found in trypanosome kinetoplasts. We demonstrate basic properties of three principal variants of this model which we show to form a strict hierarchy in terms of expressive power. We also present a method and software for simulating real biological RNA editing via this model and apply the theoretical results to suggest real biological constraints on this process.

Efficient Algorithms for Exact Inference in Sequence Labeling SVMs

The task of structured output prediction deals with learning general functional dependencies between arbitrary input and output spaces. In this context, two loss-sensitive formulations for maximum-margin training have been proposed in the literature, which are referred to as margin and slack rescaling, respectively. The latter is believed to be more accurate and easier to handle. Nevertheless, it is not popular due to the lack of known efficient inference algorithms; therefore, margin rescaling - which requires a similar type of inference as normal structured prediction - is the most often used approach. Focusing on the task of label sequence learning, we here define a general framework that can handle a large class of inference problems based on Hamming-like loss functions and the concept of decomposability for the underlying joint feature map. In particular, we present an efficient generic algorithm that can handle both rescaling approaches and is guaranteed to find an optimal solution in polynomial time.

Algorithmic decomposition of shuffle on words

We investigate shuffle-decomposability into two words. We give an algorithm which takes as input a DFA M (under certain conditions) and determines the unique candidate decomposition into words u and v such that L(M)=uv if M is shuffle decomposable, in time O(|u|+|v|). Even though this algorithm does not determine whether or not the DFA is shuffle decomposable, the sublinear time complexity of only determining the two words under the assumption of decomposability is surprising given the complexity of shuffle, and demonstrates an interesting property of the operation. We also show that for given words u and v and a DFA M we can determine whether uv@?L(M) in polynomial time.

On the Shuffle Automaton Size for Words

We investigate the state size of DFAs accepting the shuffle of two words. We provide words u and v, such that the minimal DFA for u shuffled with v requires an exponential number of states. We also show some conditions for the words u and v which ensure a quadratic upper bound on the state size of u shuffled with v. Moreover, switching only two letters within one of u or v is enough to trigger the change from quadratic to exponential.

On Comparing Deterministic Finite Automata and the Shuffle of Words

We continue the study of the shuffle of individual words, and the problem of decomposing a finite automaton into the shuffle on words. There is a known polynomial time algorithm to decide whether the shuffle of two words is a subset of the language accepted by a deterministic finite automaton [5]. In this paper, we consider the converse problem of determining whether or not the language accepted by a deterministic finite automaton is a subset of the shuffle of two words. We provide a polynomial time algorithm to decide whether the language accepted by a deterministic finite automaton is a subset of the shuffle of two words, for the special case when the skeletons of the two words are of fixed length. Therefore, for this special case, we can decide equality in polynomial time as well. However, we then show that this problem is coNP-Complete in general, as conjectured in [2].

An infinite hierarchy induced by depth synchronization

Depth-synchronization measures the number of parallel derivation steps in a synchronized context-free (SCF) grammar. When not bounded by a constant the depth-synchronization measure of an SCF grammar is at least logarithmic and at most linear with respect to the word length. Languages with linear depth-synchronization measure and languages with a depth-synchronization measure in between logarithmic and linear are proven to exist. This gives rise to a strict infinite hierarchy within the family of SCF (and ET0L) languages.

On the synchronized derivation depth of context-free grammars

We consider depth of derivations as a complexity measure for synchronized and ordinary context-free grammars. This measure differs from the earlier considered synchronization depth in that it counts the depth of the entire derivation tree. We consider (non-)existence of trade-offs when using synchronized grammars as opposed to non-synchronized grammars and establish lower bounds for certain classes of linear context-free languages.

COMPUTATION BY ANNOTATION: MODELLING EPIGENETIC REGULATION

We present a formal model inspired by the epigenetic process of gene annotation via histone modification. In particular, we study the generative capacity of a system in which annotations on a set of strings control which substrings are ultimately produced by the system and in which only the annotations, and not the strings themselves, may be rewritten. On a biological level this represents a first attempt to better understand the computational limits of this form of epigenetic regulation. We introduce two different derivation modes for our formal system and show that these systems are actually quite weak. The weaker of the derivation modes is directly capable only of generating a subset of the regular languages while the more powerful derivation mode is also only capable of generating all regular languages modulo a begin- and an end-marker.