# Tensor decomposition

Patient-derived xenografts (PDX) implant human tumors into immunocompromised mice to test drugs, but screening every tumor-drug combination is infeasible in time and cost. GrAFT-PDX is a Bayesian model that jointly models tumor growth trajectories and mouse death risk, using a low-rank tensor decomposition to share information across PDX lines, treatments and time, so it can impute untested experiments and predict death times. On the large PDXe screen it assigns higher log probability to death times than Royston-Parmar and other survival baselines, matches strong baselines on tumor response, and preserves known gene-drug associations without genomic input.

Patient-derived xenografts (PDX) implant human tumors into immunocompromised mice to test drugs, but screening every tumor-drug combination is infeasible in time and cost. GrAFT-PDX is a Bayesian model that jointly models tumor growth trajectories and mouse death risk, using a low-rank tensor decomposition to share information across PDX lines, treatments and time, so it can impute untested experiments and predict death times. On the large PDXe screen it assigns higher log probability to death times than Royston-Parmar and other survival baselines, matches strong baselines on tumor response, and preserves known gene-drug associations without genomic input.

Neuralign places neural recordings from different sessions and animals, with different sampled neurons, into one tensor decomposition in which each component shares a single temporal curve while trial strength and neuron weights are estimated per session, so no matched neurons or matched trials are needed. On 93 brain-wide recordings from 19 mice, an unsupervised fit yielded a single component that separated the three anterior lateral motor cortex (ALM) optogenetic inhibition conditions, with balanced accuracy of 0.647 on held-out sessions against a chance level of 1/3. That component's change showed a modest association with the drop in behavioural accuracy (ρ = 0.266 over 180 session–inhibition observations).

Neuralign places neural recordings from different sessions and animals, with different sampled neurons, into one tensor decomposition in which each component shares a single temporal curve while trial strength and neuron weights are estimated per session, so no matched neurons or matched trials are needed. On 93 brain-wide recordings from 19 mice, an unsupervised fit yielded a single component that separated the three anterior lateral motor cortex (ALM) optogenetic inhibition conditions, with balanced accuracy of 0.647 on held-out sessions against a chance level of 1/3. That component's change showed a modest association with the drop in behavioural accuracy (ρ = 0.266 over 180 session–inhibition observations).