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Detecting synaptic connections using large-scale extracellular spike recordings presents a statistical challenge. Although previous methods often treat the detection of each putative connection as a separate hypothesis test, here we develop a modeling approach that infers synaptic connections while incorporating circuit properties learned from the whole network. We use an extension of the generalized linear model framework to describe the cross-correlograms between pairs of neurons and separate correlograms into two parts: a slowly varying effect due to background fluctuations and a fast, transient effect due to the synapse. We then use the observations from all putative connections in the recording to estimate two network properties: the presynaptic neuron type (excitatory or inhibitory) and the relationship between synaptic latency and distance between neurons. Constraining the presynaptic neuron’s type, synaptic latencies, and time constants improves synapse detection. In data from simulated networks, this model outperforms two previously developed synapse detection methods, especially on the weak connections. We also apply our model to in vitro multielectrode array recordings from the mouse somatosensory cortex. Here, our model automatically recovers plausible connections from hundreds of neurons, and the properties of the putative connections are largely consistent with previous research. NEW & NOTEWORTHY Detecting synaptic connections using large-scale extracellular spike recordings is a difficult statistical problem. Here, we develop an extension of a generalized linear model that explicitly separates fast synaptic effects and slow background fluctuations in cross-correlograms between pairs of neurons while incorporating circuit properties learned from the whole network. This model outperforms two previously developed synapse detection methods in the simulated networks and recovers plausible connections from hundreds of neurons in in vitro multielectrode array data.