Discrete gene regulatory networks (GRNs) play a vital role in the study of robustness and modularity. A common method of evaluating the robustness of GRNs is to measure their ability to regulate a set of perturbed gene activation patterns back to their unperturbed forms. Usually, perturbations are obtained by collecting random samples produced by a predefined distribution of gene activation patterns. This sampling method introduces stochasticity, in turn inducing dynamicity. This dynamicity is imposed on top of an already complex fitness landscape. So where sampling is used, it is important to understand which effects arise from the structure of the fitness landscape, and which arise from the dynamicity imposed on it. Stochasticity of the fitness function also causes difficulties in reproducibility and in post-experimental analyses. We develop a deterministic distributional fitness evaluation by considering the complete distribution of gene activity patterns, so as to avoid stochasticity in fitness assessment. This fitness evaluation facilitates repeatability. Its determinism permits us to ascertain theoretical bounds on the fitness, and thus to identify whether the algorithm has reached a global optimum. It enables us to differentiate the effects of the problem domain from those of the noisy fitness evaluation, and thus to resolve two remaining anomalies in the behaviour of the problem domain of~\citet{espinosa2010specialization}. We also reveal some properties of solution GRNs that lead them to be robust and modular, leading to a deeper understanding of the nature of the problem domain. We conclude by discussing potential directions toward simulating and understanding the emergence of modularity in larger, more complex domains, which is key both to generating more useful modular solutions, and to understanding the ubiquity of modularity in biological systems.
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We propose nonparametric estimators for the second-order central moments of spherical random fields within a functional data context. We consider a measurement framework where each field among an identically distributed collection of spherical random fields is sampled at a few random directions, possibly subject to measurement error. The collection of fields could be i.i.d. or serially dependent. Though similar setups have already been explored for random functions defined on the unit interval, the nonparametric estimators proposed in the literature often rely on local polynomials, which do not readily extend to the (product) spherical setting. We therefore formulate our estimation procedure as a variational problem involving a generalized Tikhonov regularization term. The latter favours smooth covariance/autocovariance functions, where the smoothness is specified by means of suitable Sobolev-like pseudo-differential operators. Using the machinery of reproducing kernel Hilbert spaces, we establish representer theorems that fully characterizing the form of our estimators. We determine their uniform rates of convergence as the number of fields diverges, both for the dense (increasing number of spatial samples) and sparse (bounded number of spatial samples) regimes. We moreover validate and demonstrate the practical feasibility of our estimation procedure in a simulation setting, assuming a fixed number of samples per field. Our numerical estimation procedure leverages the sparsity and second-order Kronecker structure of our setup to reduce the computational and memory requirements by approximately three orders of magnitude compared to a naive implementation would require.
When the sizes of the state and action spaces are large, solving MDPs can be computationally prohibitive even if the probability transition matrix is known. So in practice, a number of techniques are used to approximately solve the dynamic programming problem, including lookahead, approximate policy evaluation using an m-step return, and function approximation. In a recent paper, (Efroni et al. 2019) studied the impact of lookahead on the convergence rate of approximate dynamic programming. In this paper, we show that these convergence results change dramatically when function approximation is used in conjunction with lookout and approximate policy evaluation using an m-step return. Specifically, we show that when linear function approximation is used to represent the value function, a certain minimum amount of lookahead and multi-step return is needed for the algorithm to even converge. And when this condition is met, we characterize the performance of policies obtained using such approximate policy iteration. Our results are presented for two different procedures to compute the function approximation: linear least-squares regression and gradient descent.
The central levels problem asserts that the subgraph of the $(2m+1)$-dimensional hypercube induced by all bitstrings with at least $m+1-\ell$ many 1s and at most $m+\ell$ many 1s, i.e., the vertices in the middle $2\ell$ levels, has a Hamilton cycle for any $m\geq 1$ and $1\le \ell\le m+1$. This problem was raised independently by Buck and Wiedemann, Savage, by Gregor and \v{S}krekovski, and by Shen and Williams, and it is a common generalization of the well-known middle levels problem, namely the case $\ell=1$, and classical binary Gray codes, namely the case $\ell=m+1$. In this paper we present a general constructive solution of the central levels problem. Our results also imply the existence of optimal cycles through any sequence of $\ell$ consecutive levels in the $n$-dimensional hypercube for any $n\ge 1$ and $1\le \ell \le n+1$. Moreover, extending an earlier construction by Streib and Trotter, we construct a Hamilton cycle through the $n$-dimensional hypercube, $n\geq 2$, that contains the symmetric chain decomposition constructed by Greene and Kleitman in the 1970s, and we provide a loopless algorithm for computing the corresponding Gray code.
The difficulty in specifying rewards for many real-world problems has led to an increased focus on learning rewards from human feedback, such as demonstrations. However, there are often many different reward functions that explain the human feedback, leaving agents with uncertainty over what the true reward function is. While most policy optimization approaches handle this uncertainty by optimizing for expected performance, many applications demand risk-averse behavior. We derive a novel policy gradient-style robust optimization approach, PG-BROIL, that optimizes a soft-robust objective that balances expected performance and risk. To the best of our knowledge, PG-BROIL is the first policy optimization algorithm robust to a distribution of reward hypotheses which can scale to continuous MDPs. Results suggest that PG-BROIL can produce a family of behaviors ranging from risk-neutral to risk-averse and outperforms state-of-the-art imitation learning algorithms when learning from ambiguous demonstrations by hedging against uncertainty, rather than seeking to uniquely identify the demonstrator's reward function.
Approaches based on deep neural networks have achieved striking performance when testing data and training data share similar distribution, but can significantly fail otherwise. Therefore, eliminating the impact of distribution shifts between training and testing data is crucial for building performance-promising deep models. Conventional methods assume either the known heterogeneity of training data (e.g. domain labels) or the approximately equal capacities of different domains. In this paper, we consider a more challenging case where neither of the above assumptions holds. We propose to address this problem by removing the dependencies between features via learning weights for training samples, which helps deep models get rid of spurious correlations and, in turn, concentrate more on the true connection between discriminative features and labels. Extensive experiments clearly demonstrate the effectiveness of our method on multiple distribution generalization benchmarks compared with state-of-the-art counterparts. Through extensive experiments on distribution generalization benchmarks including PACS, VLCS, MNIST-M, and NICO, we show the effectiveness of our method compared with state-of-the-art counterparts.
A key challenge of big data analytics is how to collect a large volume of (labeled) data. Crowdsourcing aims to address this challenge via aggregating and estimating high-quality data (e.g., sentiment label for text) from pervasive clients/users. Existing studies on crowdsourcing focus on designing new methods to improve the aggregated data quality from unreliable/noisy clients. However, the security aspects of such crowdsourcing systems remain under-explored to date. We aim to bridge this gap in this work. Specifically, we show that crowdsourcing is vulnerable to data poisoning attacks, in which malicious clients provide carefully crafted data to corrupt the aggregated data. We formulate our proposed data poisoning attacks as an optimization problem that maximizes the error of the aggregated data. Our evaluation results on one synthetic and two real-world benchmark datasets demonstrate that the proposed attacks can substantially increase the estimation errors of the aggregated data. We also propose two defenses to reduce the impact of malicious clients. Our empirical results show that the proposed defenses can substantially reduce the estimation errors of the data poisoning attacks.
Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and often assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to bound the end-to-end privacy loss. The theoretical analysis shows that DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee.
Generative adversarial nets (GANs) have generated a lot of excitement. Despite their popularity, they exhibit a number of well-documented issues in practice, which apparently contradict theoretical guarantees. A number of enlightening papers have pointed out that these issues arise from unjustified assumptions that are commonly made, but the message seems to have been lost amid the optimism of recent years. We believe the identified problems deserve more attention, and highlight the implications on both the properties of GANs and the trajectory of research on probabilistic models. We recently proposed an alternative method that sidesteps these problems.
We demonstrate that many detection methods are designed to identify only a sufficently accurate bounding box, rather than the best available one. To address this issue we propose a simple and fast modification to the existing methods called Fitness NMS. This method is tested with the DeNet model and obtains a significantly improved MAP at greater localization accuracies without a loss in evaluation rate, and can be used in conjunction with Soft NMS for additional improvements. Next we derive a novel bounding box regression loss based on a set of IoU upper bounds that better matches the goal of IoU maximization while still providing good convergence properties. Following these novelties we investigate RoI clustering schemes for improving evaluation rates for the DeNet wide model variants and provide an analysis of localization performance at various input image dimensions. We obtain a MAP of 33.6%@79Hz and 41.8%@5Hz for MSCOCO and a Titan X (Maxwell). Source code available from: //github.com/lachlants/denet
Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well without careful hyperparameter tuning and proper initialization. We investigate whether turning the adversarial min-max problem into an optimization problem by replacing the maximization part with its dual improves the quality of the resulting alignment and explore its connections to Maximum Mean Discrepancy. Our empirical results suggest that using the dual formulation for the restricted family of linear discriminators results in a more stable convergence to a desirable solution when compared with the performance of a primal min-max GAN-like objective and an MMD objective under the same restrictions. We test our hypothesis on the problem of aligning two synthetic point clouds on a plane and on a real-image domain adaptation problem on digits. In both cases, the dual formulation yields an iterative procedure that gives more stable and monotonic improvement over time.
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