instruction:
In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
question:
Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One motivating application is drug development: morphological cell features can be captured from images, from which similarities between different drugs applied at different dosages can be quantified. The general approach is to find a function mapping the images to an embedding space of manageable dimensionality whose geometry captures relevant features of the input images. An important known issue for such methods is separating relevant biological signal from nuisance variation. For example, the embedding vectors tend to be more correlated for cells that were cultured and imaged during the same week than for cells from a different week, despite having identical drug compounds applied in both cases. In this case, the particular batch a set of experiments were conducted in constitutes the domain of the data; an ideal set of image embeddings should contain only the relevant biological information (e.g. drug effects). We develop a general framework for adjusting the image embeddings in order to `forget' domain-specific information while preserving relevant biological information. To do this, we minimize a loss function based on distances between marginal distributions (such as the Wasserstein distance) of embeddings across domains for each replicated treatment. For the dataset presented, the replicated treatment is the negative control. We find that for our transformed embeddings (1) the underlying geometric structure is not only preserved but the embeddings also carry improved biological signal (2) less domain-specific information is present.
answer:
We correct nuisance variation for image embeddings across different domains, preserving only relevant information.


question:
Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we propose Deep Random Splines, a flexible class of random functions obtained by transforming Gaussian noise through a deep neural network whose output are the parameters of a spline. Unlike Gaussian processes, Deep Random Splines allow us to readily enforce shape constraints while inheriting the richness and tractability of deep generative models. We also present an observational model for point process data which uses Deep Random Splines to model the intensity function of each point process and apply it to neuroscience data to obtain a low-dimensional representation of spiking activity. Inference is performed via a variational autoencoder that uses a novel recurrent encoder architecture that can handle multiple point processes as input.
answer:
We combine splines with neural networks to obtain a novel distribution over functions and use it to model intensity functions of point processes.


question:
Bayesian neural networks, which both use the negative log-likelihood loss function and average their predictions using a learned posterior over the parameters, have been used successfully across many scientific fields, partly due to their ability to `effortlessly' extract desired representations from many large-scale datasets. However, generalization bounds for this setting is still missing.
 In this paper, we present a new PAC-Bayesian generalization bound for the negative log-likelihood loss which utilizes the \emph{Herbst Argument} for the log-Sobolev inequality to bound the moment generating function of the learners risk.
answer:

We derive a new PAC-Bayesian Bound for unbounded loss functions (e.g. Negative Log-Likelihood).