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Is this true for the class of methods that regularize the difference between two graphs (e.g.

Rationally identifying variables responsible for changes to a biological system can enable myriad applications in disease understanding and cell engineering. From a causality perspective, we are given two datasets generated by the same causal model, one observational (control) and one interventional (perturbed). The goal is to isolate the subset of measured variables (e.g. genes) that were the targets of the intervention, i.e. those whose conditional independencies have changed. Knowing the causal graph would limit the search space, allowing us to efficiently pinpoint these variables. However, current algorithms that infer causal graphs in the presence of unknown intervention targets scale poorly to the hundreds or thousands of variables in biological data, as they must jointly search the combinatorial spaces of graphs and consistent intervention targets. In this work, we propose a causality-inspired approach for predicting perturbation targets that decouples the two search steps. First, we use an amortized causal discovery model to separately infer causal graphs from the observational and interventional datasets. Then, we learn to map these paired graphs to the sets of variables that were intervened upon, in a supervised learning framework. This approach consistently outperforms baselines for perturbation modeling on seven single-cell transcriptomics datasets, each with thousands of measured variables. We also demonstrate significant improvements over six causal discovery algorithms in predicting intervention targets across a variety of tractable, synthetic datasets.

We assume a multi-source and heterogeneous dataset is available for each class, where the covariance matrices are identical for all non-paranormal graphical models. The differential network, which are encoded by the difference precision matrix, can then be decoded by optimizing a lasso penalized D-trace loss function. To this aim, an efficient approach is proposed that outputs the exact solution path, outperforming the previous methods that only sample from the solution path in pre-selected regularization parameters. Notably, our proposed method has low computational complexity, especially when the differential network are sparse. Our simulations on synthetic data demonstrate a superior performance for our strategy in terms of speed and accuracy compared to an existing method. Moreover, our strategy in combining datasets from multiple sources is shown to be very effective in inferring differential network in real-world problems. This is backed by our experimental results on drug resistance in tumor cancers. In the latter case, our strategy outputs important genes for drug resistance which are already confirmed by various independent studies.

In many cases of network analysis, it is more attractive to study how a network varies under different conditions than an individual static network. We propose a novel graphical model, namely Latent Differential Graph Model, where the networks under two different conditions are represented by two semiparametric elliptical distributions respectively, and the variation of these two networks (i.e., differential graph) is characterized by the difference between their latent precision matrices. We propose an estimator for the differential graph based on quasi likelihood maximization with nonconvex regularization. We show that our estimator attains a faster statistical rate in parameter estimation than the state-of-the-art methods, and enjoys the oracle property under mild conditions. Thorough experiments on both synthetic and real world data support our theory.

Gaussian graphical models (Lauritzen, 1996) are used to capture complex relationships among observed variables in a variety of fields, ranging from computational biology (Friedman, 2004), genetics (Lauritzen and Sheehan, 2003), to neuroscience (Smith et al., 2011). Each node in a graphical model represents an observed variable and the (undirected) edge between two nodes is present if the nodes are conditionally dependent given all the other variables; thus (sparse) graphical models are highly interpretable and have been adopted for a wide variety of applications. Of particular interest in this manuscript are applications to cognitive neuroscience, specifically functional connectivity; the study of functional interactions between brain regions, thought to be necessary for cognition (Bullmore and Sporns, 2009). Importantly, functional connectivity is a promising biomarker for mental disorders (Castellanos et al., 2013), where the primary object of study is the differential network, that is the differences in connectivity between healthy individuals and patients. See Bielza and Larrañaga (2014) for a detailed review.

Learning optimal feedback control laws capable of executing optimal trajectories is essential for many robotic applications. Such policies can be learned using reinforcement learning or planned using optimal control. While reinforcement learning is sample inefficient, optimal control only plans an optimal trajectory from a specific starting configuration. In this paper we propose deep optimal feedback control to learn an optimal feedback policy rather than a single trajectory. By exploiting the inherent structure of the robot dynamics and strictly convex action cost, we can derive principled cost functions such that the optimal policy naturally obeys the action limits, is globally optimal and stable on the training domain given the optimal value function. The corresponding optimal value function is learned end-to-end by embedding a deep differential network in the Hamilton-Jacobi-Bellmann differential equation and minimizing the error of this equality while simultaneously decreasing the discounting from short- to far-sighted to enable the learning. Our proposed approach enables us to learn an optimal feedback control law in continuous time, that in contrast to existing approaches generates an optimal trajectory from any point in state-space without the need of replanning. The resulting approach is evaluated on non-linear systems and achieves optimal feedback control, where standard optimal control methods require frequent replanning.

In many cases of network analysis, it is more attractive to study how a network varies under different conditions than an individual static network. We propose a novel graphical model, namely Latent Differential Graph Model, where the networks under two different conditions are represented by two semiparametric elliptical distributions respectively, and the variation of these two networks (i.e., differential graph) is characterized by the difference between their latent precision matrices. We propose an estimator for the differential graph based on quasi likelihood maximization with nonconvex regularization. We show that our estimator attains a faster statistical rate in parameter estimation than the state-of-the-art methods, and enjoys oracle property under mild conditions. Thorough experiments on both synthetic and real world data support our theory.

We study the problem of learning sparse structure changes between two Markov networks $P$ and $Q$. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes \emph{directly} via estimating the ratio between two Markov network models. In this paper, we give sufficient conditions for \emph{successful change detection} with respect to the sample size $n_p, n_q$, the dimension of data $m$, and the number of changed edges $d$. When using an unbounded density ratio model we prove that the true sparse changes can be consistently identified for $n_p = \Omega(d^2 \log \frac{m^2+m}{2})$ and $n_q = \Omega({n_p^2})$, with an exponentially decaying upper-bound on learning error. Such sample complexity can be improved to $\min(n_p, n_q) = \Omega(d^2 \log \frac{m^2+m}{2})$ when the boundedness of the density ratio model is assumed. Our theoretical guarantee can be applied to a wide range of discrete/continuous Markov networks.