TY - JOUR
AB - The Ising model is one of the simplest and most famous models of interacting systems. It was originally proposed to model ferromagnetic interactions in statistical physics and is now widely used to model spatial processes in many areas such as ecology, sociology, and genetics, usually without testing its goodness-of-fit. Here, we propose an exact goodness-of-fit test for the finite-lattice Ising model. The theory of Markov bases has been developed in algebraic statistics for exact goodness-of-fit testing using a Monte Carlo approach. However, this beautiful theory has fallen short of its promise for applications, because finding a Markov basis is usually computationally intractable. We develop a Monte Carlo method for exact goodness-of-fit testing for the Ising model which avoids computing a Markov basis and also leads to a better connectivity of the Markov chain and hence to a faster convergence. We show how this method can be applied to analyze the spatial organization of receptors on the cell membrane.
AU - Martin Del Campo Sanchez, Abraham
AU - Cepeda Humerez, Sarah A
AU - Uhler, Caroline
ID - 2016
IS - 2
JF - Scandinavian Journal of Statistics
SN - 03036898
TI - Exact goodness-of-fit testing for the Ising model
VL - 44
ER -
TY - JOUR
AB - Advances in multi-unit recordings pave the way for statistical modeling of activity patterns in large neural populations. Recent studies have shown that the summed activity of all neurons strongly shapes the population response. A separate recent finding has been that neural populations also exhibit criticality, an anomalously large dynamic range for the probabilities of different population activity patterns. Motivated by these two observations, we introduce a class of probabilistic models which takes into account the prior knowledge that the neural population could be globally coupled and close to critical. These models consist of an energy function which parametrizes interactions between small groups of neurons, and an arbitrary positive, strictly increasing, and twice differentiable function which maps the energy of a population pattern to its probability. We show that: 1) augmenting a pairwise Ising model with a nonlinearity yields an accurate description of the activity of retinal ganglion cells which outperforms previous models based on the summed activity of neurons; 2) prior knowledge that the population is critical translates to prior expectations about the shape of the nonlinearity; 3) the nonlinearity admits an interpretation in terms of a continuous latent variable globally coupling the system whose distribution we can infer from data. Our method is independent of the underlying system’s state space; hence, it can be applied to other systems such as natural scenes or amino acid sequences of proteins which are also known to exhibit criticality.
AU - Humplik, Jan
AU - Tkacik, Gasper
ID - 720
IS - 9
JF - PLoS Computational Biology
SN - 1553734X
TI - Probabilistic models for neural populations that naturally capture global coupling and criticality
VL - 13
ER -
TY - JOUR
AB - Individual computations and social interactions underlying collective behavior in groups of animals are of great ethological, behavioral, and theoretical interest. While complex individual behaviors have successfully been parsed into small dictionaries of stereotyped behavioral modes, studies of collective behavior largely ignored these findings; instead, their focus was on inferring single, mode-independent social interaction rules that reproduced macroscopic and often qualitative features of group behavior. Here, we bring these two approaches together to predict individual swimming patterns of adult zebrafish in a group. We show that fish alternate between an “active” mode, in which they are sensitive to the swimming patterns of conspecifics, and a “passive” mode, where they ignore them. Using a model that accounts for these two modes explicitly, we predict behaviors of individual fish with high accuracy, outperforming previous approaches that assumed a single continuous computation by individuals and simple metric or topological weighing of neighbors’ behavior. At the group level, switching between active and passive modes is uncorrelated among fish, but correlated directional swimming behavior still emerges. Our quantitative approach for studying complex, multi-modal individual behavior jointly with emergent group behavior is readily extensible to additional behavioral modes and their neural correlates as well as to other species.
AU - Harpaz, Roy
AU - Tkacik, Gasper
AU - Schneidman, Elad
ID - 725
IS - 38
JF - PNAS
SN - 00278424
TI - Discrete modes of social information processing predict individual behavior of fish in a group
VL - 114
ER -
TY - JOUR
AB - Neural responses are highly structured, with population activity restricted to a small subset of the astronomical range of possible activity patterns. Characterizing these statistical regularities is important for understanding circuit computation, but challenging in practice. Here we review recent approaches based on the maximum entropy principle used for quantifying collective behavior in neural activity. We highlight recent models that capture population-level statistics of neural data, yielding insights into the organization of the neural code and its biological substrate. Furthermore, the MaxEnt framework provides a general recipe for constructing surrogate ensembles that preserve aspects of the data, but are otherwise maximally unstructured. This idea can be used to generate a hierarchy of controls against which rigorous statistical tests are possible.
AU - Savin, Cristina
AU - Tkacik, Gasper
ID - 730
JF - Current Opinion in Neurobiology
SN - 09594388
TI - Maximum entropy models as a tool for building precise neural controls
VL - 46
ER -
TY - JOUR
AB - Cell-cell contact formation constitutes an essential step in evolution, leading to the differentiation of specialized cell types. However, remarkably little is known about whether and how the interplay between contact formation and fate specification affects development. Here, we identify a positive feedback loop between cell-cell contact duration, morphogen signaling, and mesendoderm cell-fate specification during zebrafish gastrulation. We show that long-lasting cell-cell contacts enhance the competence of prechordal plate (ppl) progenitor cells to respond to Nodal signaling, required for ppl cell-fate specification. We further show that Nodal signaling promotes ppl cell-cell contact duration, generating a positive feedback loop between ppl cell-cell contact duration and cell-fate specification. Finally, by combining mathematical modeling and experimentation, we show that this feedback determines whether anterior axial mesendoderm cells become ppl or, instead, turn into endoderm. Thus, the interdependent activities of cell-cell signaling and contact formation control fate diversification within the developing embryo.
AU - Barone, Vanessa
AU - Lang, Moritz
AU - Krens, Gabriel
AU - Pradhan, Saurabh
AU - Shamipour, Shayan
AU - Sako, Keisuke
AU - Sikora, Mateusz K
AU - Guet, Calin C
AU - Heisenberg, Carl-Philipp J
ID - 735
IS - 2
JF - Developmental Cell
SN - 15345807
TI - An effective feedback loop between cell-cell contact duration and morphogen signaling determines cell fate
VL - 43
ER -