arXiv subjects

Riccardo Zecchina

Publications and source records attributed to Riccardo Zecchina.

At least 55 records · Page 3Linked to original sources

arXiv2014

Fast and accurate multivariate Gaussian modeling of protein families: Predicting residue contacts and protein-interaction partners

In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our method aims at extracting such constraints from rapidly accumulating sequence data, and thereby at inferring protein structure and function from sequence information alone. Recently, global statistical inference methods (e.g. direct-coupling analysis, sparse inverse covariance estimation) have achieved a breakthrough towards this aim, and their predictions have been successfully implemented into tertiary and quaternary protein structure prediction methods. However, due to the discrete nature of the underlying variable (amino-acids), exact inference requires exponential time in the protein length, and efficient approximations are needed for practical applicability. Here we propose a very efficient multivariate Gaussian modeling approach as a variant of direct-coupling analysis: the discrete amino-acid variables are replaced by continuous Gaussian random variables. The resulting statistical inference problem is efficiently and exactly solvable. We show that the quality of inference is comparable or superior to the one achieved by mean-field approximations to inference with discrete variables, as done by direct-coupling analysis. This is true for (i) the prediction of residue-residue contacts in proteins, and (ii) the identification of protein-protein interaction partner in bacterial signal transduction. An implementation of our multivariate Gaussian approach is available at the website http://areeweb.polito.it/ricerca/cmp/code

q-bio.QM↗

arXiv2014

Bayesian inference of epidemics on networks via Belief Propagation

We study several bayesian inference problems for irreversible stochastic epidemic models on networks from a statistical physics viewpoint. We derive equations which allow to accurately compute the posterior distribution of the time evolution of the state of each node given some observations. At difference with most existing methods, we allow very general observation models, including unobserved nodes, state observations made at different or unknown times, and observations of infection times, possibly mixed together. Our method, which is based on the Belief Propagation algorithm, is efficient, naturally distributed, and exact on trees. As a particular case, we consider the problem of finding the "zero patient" of a SIR or SI epidemic given a snapshot of the state of the network at a later unknown time. Numerical simulations show that our method outperforms previous ones on both synthetic and real networks, often by a very large margin.

q-bio.QM↗

arXiv2013

Theory and learning protocols for the material tempotron model

Neural networks are able to extract information from the timing of spikes. Here we provide new results on the behavior of the simplest neuronal model which is able to decode information embedded in temporal spike patterns, the so called tempotron. Using statistical physics techniques we compute the capacity for the case of sparse, time-discretized input, and "material" discrete synapses, showing that the device saturates the information theoretic bounds with a statistics of output spikes that is consistent with the statistics of the inputs. We also derive two simple and highly efficient learning algorithms which are able to learn a number of associations which are close to the theoretical limit. The simplest versions of these algorithms correspond to distributed on-line protocols of interest for neuromorphic devices, and can be adapted to address the more biologically relevant continuous-time version of the classification problem, hopefully allowing for the understanding of some aspects of synaptic plasticity.

cond-mat.dis-nn↗

arXiv2013

On the performance of a cavity method based algorithm for the Prize-Collecting Steiner Tree Problem on graphs

We study the behavior of an algorithm derived from the cavity method for the Prize-Collecting Steiner Tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks networks and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the DHEA solver, a Branch and Cut Linear/Integer Programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two post-processing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.

cs.DS↗

arXiv2013

Perturbation Biology: inferring signaling networks in cellular systems

We present a new experimental-computational technology of inferring network models that predict the response of cells to perturbations and that may be useful in the design of combinatorial therapy against cancer. The experiments are systematic series of perturbations of cancer cell lines by targeted drugs, singly or in combination. The response to perturbation is measured in terms of levels of proteins and phospho-proteins and of cellular phenotype such as viability. Computational network models are derived de novo, i.e., without prior knowledge of signaling pathways, and are based on simple non-linear differential equations. The prohibitively large solution space of all possible network models is explored efficiently using a probabilistic algorithm, belief propagation, which is three orders of magnitude more efficient than Monte Carlo methods. Explicit executable models are derived for a set of perturbation experiments in Skmel-133 melanoma cell lines, which are resistant to the therapeutically important inhibition of Raf kinase. The resulting network models reproduce and extend known pathway biology. They can be applied to discover new molecular interactions and to predict the effect of novel drug perturbations, one of which is verified experimentally. The technology is suitable for application to larger systems in diverse areas of molecular biology.

q-bio.MN↗

arXiv2013

Optimizing spread dynamics on graphs by message passing

Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the last decades, many efforts have been devoted to understand the typical behaviour of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception of models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network).

cond-mat.dis-nn↗

arXiv2012

Modeling competing endogenous RNAs networks

MicroRNAs (miRNAs) are small RNA molecules, about 22 nucleotide long, which post-transcriptionally regulate their target messenger RNAs (mRNAs). They accomplish key roles in gene regulatory networks, ranging from signaling pathways to tissue morphogenesis, and their aberrant behavior is often associated with the development of various diseases. Recently it has been shown that, in analogy with the better understood case of small RNAs in bacteria, the way miRNAs interact with their targets can be described in terms of a titration mechanism characterized by threshold effects, hypersensitivity of the system near the threshold, and prioritized cross-talk among targets. The latter characteristic has been lately identified as competing endogenous RNA (ceRNA) effect to mark those indirect interactions among targets of a common pool of miRNAs they are in competition for. Here we analyze the equilibrium and out-of-equilibrium properties of a general stochastic model of $M$ miRNAs interacting with $N$ mRNA targets. In particular we are able to describe in details the peculiar equilibrium and non-equilibrium phenomena that the system displays around the threshold: (i) maximal cross-talk and correlation between targets, (ii) robustness of ceRNA effect with respect to the model's parameters and in particular to the catalyticity of the miRNA-mRNA interaction, and (iii) anomalous response-time to external perturbations.

q-bio.MN↗

arXiv2012

Message passing for quantified Boolean formulas

We introduce two types of message passing algorithms for quantified Boolean formulas (QBF). The first type is a message passing based heuristics that can prove unsatisfiability of the QBF by assigning the universal variables in such a way that the remaining formula is unsatisfiable. In the second type, we use message passing to guide branching heuristics of a Davis-Putnam Logemann-Loveland (DPLL) complete solver. Numerical experiments show that on random QBFs our branching heuristics gives robust exponential efficiency gain with respect to the state-of-art solvers. We also manage to solve some previously unsolved benchmarks from the QBFLIB library. Apart from this our study sheds light on using message passing in small systems and as subroutines in complete solvers.

cs.AI↗

arXiv2011

3D Protein Structure Predicted from Sequence

The evolutionary trajectory of a protein through sequence space is constrained by function and three-dimensional (3D) structure. Residues in spatial proximity tend to co-evolve, yet attempts to invert the evolutionary record to identify these constraints and use them to computationally fold proteins have so far been unsuccessful. Here, we show that co-variation of residue pairs, observed in a large protein family, provides sufficient information to determine 3D protein structure. Using a data-constrained maximum entropy model of the multiple sequence alignment, we identify pairs of statistically coupled residue positions which are expected to be close in the protein fold, termed contacts inferred from evolutionary information (EICs). To assess the amount of information about the protein fold contained in these coupled pairs, we evaluate the accuracy of predicted 3D structures for proteins of 50-260 residues, from 15 diverse protein families, including a G-protein coupled receptor. These structure predictions are de novo, i.e., they do not use homology modeling or sequence-similar fragments from known structures. The resulting low Cα-RMSD error range of 2.7-5.1Å, over at least 75% of the protein, indicates the potential for predicting essentially correct 3D structures for the thousands of protein families that have no known structure, provided they include a sufficiently large number of divergent sample sequences. With the current enormous growth in sequence information based on new sequencing technology, this opens the door to a comprehensive survey of protein 3D structures, including many not currently accessible to the experimental methods of structural genomics. This advance has potential applications in many biological contexts, such as synthetic biology, identification of functional sites in proteins and interpretation of the functional impact of genetic variants.

q-bio.BM↗

arXiv2011

Direct-coupling analysis of residue co-evolution captures native contacts across many protein families

The similarity in the three-dimensional structures of homologous proteins imposes strong constraints on their sequence variability. It has long been suggested that the resulting correlations among amino acid compositions at different sequence positions can be exploited to infer spatial contacts within the tertiary protein structure. Crucial to this inference is the ability to disentangle direct and indirect correlations, as accomplished by the recently introduced Direct Coupling Analysis (DCA) (Weigt et al. (2009) Proc Natl Acad Sci 106:67). Here we develop a computationally efficient implementation of DCA, which allows us to evaluate the accuracy of contact prediction by DCA for a large number of protein domains, based purely on sequence information. DCA is shown to yield a large number of correctly predicted contacts, recapitulating the global structure of the contact map for the majority of the protein domains examined. Furthermore, our analysis captures clear signals beyond intra- domain residue contacts, arising, e.g., from alternative protein conformations, ligand- mediated residue couplings, and inter-domain interactions in protein oligomers. Our findings suggest that contacts predicted by DCA can be used as a reliable guide to facilitate computational predictions of alternative protein conformations, protein complex formation, and even the de novo prediction of protein domain structures, provided the existence of a large number of homologous sequences which are being rapidly made available due to advances in genome sequencing.

q-bio.QM↗

arXiv2011

Efficient data compression from statistical physics of codes over finite fields

In this paper we discuss a novel data compression technique for binary symmetric sources based on the cavity method over a Galois Field of order q (GF(q)). We present a scheme of low complexity and near optimal empirical performance. The compression step is based on a reduction of sparse low density parity check codes over GF(q) and is done through the so called reinforced belief-propagation equations. These reduced codes appear to have a non-trivial geometrical modification of the space of codewords which makes such compression computationally feasible. The computational complexity is O(d.n.q.log(q)) per iteration, where d is the average degree of the check nodes and n is the number of bits. For our code ensemble, decompression can be done in a time linear in the code's length by a simple leaf-removal algorithm.

cs.IT↗

arXiv2011

Efficient LDPC Codes over GF(q) for Lossy Data Compression

In this paper we consider the lossy compression of a binary symmetric source. We present a scheme that provides a low complexity lossy compressor with near optimal empirical performance. The proposed scheme is based on b-reduced ultra-sparse LDPC codes over GF(q). Encoding is performed by the Reinforced Belief Propagation algorithm, a variant of Belief Propagation. The computational complexity at the encoder is O( .n.q.log q), where is the average degree of the check nodes. For our code ensemble, decoding can be performed iteratively following the inverse steps of the leaf removal algorithm. For a sparse parity-check matrix the number of needed operations is O(n).

cs.IT↗

arXiv2011

Statistical physics of optimization under uncertainty

Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and natural sciences. We propose a general approach to solve such large-scale stochastic optimization problems and a Survey Propagation based algorithm that implements it. In the problems we consider some of the parameters are not known at the time of the first optimization, but are extracted later independently of each other from known distributions. As an illustration, we apply our method to the stochastic bipartite matching problem, in the two-stage and multi-stage cases. The efficiency of our approach, which does not rely on sampling techniques, allows us to validate the analytical predictions with large-scale numerical simulations.

cond-mat.stat-mech↗

arXiv2011

Stochastic optimization by message passing

Most optimization problems in applied sciences realistically involve uncertainty in the parameters defining the cost function, of which only statistical information is known beforehand. In a recent work we introduced a message passing algorithm based on the cavity method of statistical physics to solve the two-stage matching problem with independently distributed stochastic parameters. In this paper we provide an in-depth explanation of the general method and caveats, show the details of the derivation and resulting algorithm for the matching problem and apply it to a stochastic version of the independent set problem, which is a computationally hard and relevant problem in communication networks. We compare the results with some greedy algorithms and briefly discuss the extension to more complicated stochastic multi-stage problems.

cond-mat.stat-mech↗

arXiv2011

Belief-Propagation for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs with Integer Solutions

We consider the general problem of finding the minimum weight $\bm$-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP) algorithm converges to the correct solution. We also show that when the LP relaxation has a fractional solution then the BP algorithm can be used to solve the LP relaxation. Our proof is based on the notion of graph covers and extends the analysis of (Bayati-Shah-Sharma 2005 and Huang-Jebara 2007}. These results are notable in the following regards: (1) It is one of a very small number of proofs showing correctness of BP without any constraint on the graph structure. (2) Variants of the proof work for both synchronous and asynchronous BP; it is the first proof of convergence and correctness of an asynchronous BP algorithm for a combinatorial optimization problem.

cs.IT↗

arXiv2011

The stochastic matching problem

The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the deterministic case can be solved in polynomial time, stochastic variants are worst-case intractable. We propose an efficient method to solve stochastic matching problems which combines some features of the survey propagation equations and of the cavity method. We test it on random bipartite graphs, for which we analyze the phase diagram and compare the results with exact bounds. Our approach is shown numerically to be effective on the full range of parameters, and to outperform state-of-the-art methods. Finally we discuss how the method can be generalized to other problems of optimization under uncertainty.

cond-mat.stat-mech↗

arXiv2007

Pairs of SAT Assignment in Random Boolean Formulae

We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp threshold for this property as a function of the clause density. For large enough K, we prove that there exists a region of clause density, below the satisfiability threshold, where the landscape of Hamming distances between SAT assignments experiences a gap: pairs of SAT-assignments exist at small x, and around x=1/2, but they donot exist at intermediate values of x. This result is consistent with the clustering scenario which is at the heart of the recent heuristic analysis of satisfiability using statistical physics analysis (the cavity method), and its algorithmic counterpart (the survey propagation algorithm). The method uses elementary probabilistic arguments (first and second moment methods), and might be useful in other problems of computational and physical interest where similar phenomena appear.

cond-mat.dis-nn↗

arXiv2007

Efficient supervised learning in networks with binary synapses

Recent experimental studies indicate that synaptic changes induced by neuronal activity are discrete jumps between a small number of stable states. Learning in systems with discrete synapses is known to be a computationally hard problem. Here, we study a neurobiologically plausible on-line learning algorithm that derives from Belief Propagation algorithms. We show that it performs remarkably well in a model neuron with binary synapses, and a finite number of `hidden' states per synapse, that has to learn a random classification task. Such system is able to learn a number of associations close to the theoretical limit, in time which is sublinear in system size. This is to our knowledge the first on-line algorithm that is able to achieve efficiently a finite number of patterns learned per binary synapse. Furthermore, we show that performance is optimal for a finite number of hidden states which becomes very small for sparse coding. The algorithm is similar to the standard `perceptron' learning algorithm, with an additional rule for synaptic transitions which occur only if a currently presented pattern is `barely correct'. In this case, the synaptic changes are meta-plastic only (change in hidden states and not in actual synaptic state), stabilizing the synapse in its current state. Finally, we show that a system with two visible states and K hidden states is much more robust to noise than a system with K visible states. We suggest this rule is sufficiently simple to be easily implemented by neurobiological systems or in hardware.

q-bio.NC↗