A two-step learning approach for solving full and almost full cold start problems in dyadic prediction

Dyadic prediction methods operate on pairs of objects (dyads), aiming to infer labels for out-of-sample dyads. We consider the full and almost full cold start problem in dyadic prediction, a setting that occurs when both objects in an out-of-sample dyad have not been observed during training, or if one of them has been observed, but very few times. A popular approach for addressing this problem is to train a model that makes predictions based on a pairwise feature representation of the dyads, or, in case of kernel methods, based on a tensor product pairwise kernel. As an alternative to such a kernel approach, we introduce a novel two-step learning algorithm that borrows ideas from the fields of pairwise learning and spectral filtering. We show theoretically that the two-step method is very closely related to the tensor product kernel approach, and experimentally that it yields a slightly better predictive performance. Moreover, unlike existing tensor product kernel methods, the two-step method allows closed-form solutions for training and parameter selection via cross-validation estimates both in the full and almost full cold start settings, making the approach much more efficient and straightforward to implement

Scale-free energy dissipation and dynamic phase transition in stochastic sandpiles

We study numerically scaling properties of the distribution of cumulative energy dissipated in an avalanche and the dynamic phase transition in a stochastic directed cellular automaton [B. Tadi\'c and D. Dhar, Phys. Rev. Lett. {\bf 79}, 1519 (1997)] in d=1+1 dimensions. In the critical steady state occurring for the probability of toppling $p\ge p^\star$= 0.70548, the dissipated energy distribution exhibits scaling behavior with new scaling exponents $\tau_E$ and D_E for slope and cut-off energy, respectively, indicating that the sandpile surface is a fractal. In contrast to avalanche exponents, the energy exponents appear to be p- dependent in the region $p^\star \le p <1$, however the product $(\tau_E-1)D_E$ remains universal. We estimate the roughness exponent of the transverse section of the pile as $\chi =0.44\pm 0.04$. Critical exponents characterizing the dynamic phase transition at $p^\star$ are obtained by direct simulation and scaling analysis of the survival probability distribution and the average outflow current. The transition belongs to a new universality class with the critical exponents $\nu_\| =\gamma =1.22 \pm 0.02$, $\beta =0.56\pm 0.02$ and $\nu_\bot = 0.761 \pm 0.029$, with apparent violation of hyperscaling. Generalized hyperscaling relation leads to $\beta + \beta ^\prime = (d-1)\nu_\bot$, where $\beta ^\prime = 0.195 \pm 0.012$ is the exponent governed by the ultimate survival probability

Crossover phenomenon in self-organized critical sandpile models

We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a crossover to the scaling behavior of a different sandpile model takes place where the sand-grains are equally transferred to the nearest neighbors. The crossover behavior is numerically analyzed in detail, especially we consider the exponents which determine the scaling behavior.Comment: 6 pages, 9 figures, accepted for publication in Physical Review

Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model

We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional square lattice of lattice sizes up to L=4096. A detailed analysis of the probability distribution of the size, area, duration and radius of the avalanches will be given. To increase the accuracy of the determination of the avalanche exponents we introduce a new method for analyzing the data which reduces the finite-size effects of the measurements. The exponents of the avalanche distributions differ slightly from previous measurements and estimates obtained from a renormalization group approach.Comment: 6 pages, 6 figure

The Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension

We consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in different dimensions (D>=6). A finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents, the dynamical exponent, and the dimension of the avalanches. Above the upper critical dimension D_u=4 the exponents equal the known mean field values. An analysis of the area probability distributions indicates that the avalanches are fractal above the critical dimension.Comment: 7 pages, including 9 figures, accepted for publication in Physical Review

Mean-field behavior of the sandpile model below the upper critical dimension

We present results of large scale numerical simulations of the Bak, Tang and Wiesenfeld sandpile model. We analyze the critical behavior of the model in Euclidean dimensions $2\leq d\leq 6$. We consider a dissipative generalization of the model and study the avalanche size and duration distributions for different values of the lattice size and dissipation. We find that the scaling exponents in $d=4$ significantly differ from mean-field predictions, thus suggesting an upper critical dimension $d_c\geq 5$. Using the relations among the dissipation rate $\epsilon$ and the finite lattice size $L$, we find that a subset of the exponents displays mean-field values below the upper critical dimensions. This behavior is explained in terms of conservation laws.Comment: 4 RevTex pages, 2 eps figures embedde

Sandpile Model with Activity Inhibition

A new sandpile model is studied in which bonds of the system are inhibited for activity after a certain number of transmission of grains. This condition impels an unstable sand column to distribute grains only to those neighbours which have toppled less than m times. In this non-Abelian model grains effectively move faster than the ordinary diffusion (super-diffusion). A novel system size dependent cross-over from Abelian sandpile behaviour to a new critical behaviour is observed for all values of the parameter m.Comment: 11 pages, RevTex, 5 Postscript figure

Semi-supervised multi-task learning for predicting interactions between HIV-1 and human proteins

Motivation: Protein–protein interactions (PPIs) are critical for virtually every biological function. Recently, researchers suggested to use supervised learning for the task of classifying pairs of proteins as interacting or not. However, its performance is largely restricted by the availability of truly interacting proteins (labeled). Meanwhile, there exists a considerable amount of protein pairs where an association appears between two partners, but not enough experimental evidence to support it as a direct interaction (partially labeled)

Moment analysis of the probability distributions of different sandpile models

We reconsider the moment analysis of the Bak-Tang-Wiesenfeld and the Manna sandpile model in two and three dimensions. In contrast to recently performed investigations our analysis turns out that the models are characterized by different scaling behavior, i.e., they belong to different universality classes.Comment: 6 pages, 6 figures, accepted for publication in Physical Review