In real world settings, numerous constraints are present which are hard to specify mathematically. However, for the real world deployment of reinforcement learning (RL), it is critical that RL agents are aware of these constraints, so that they can act safely. In this work, we consider the problem of learning constraints from demonstrations of a constraint-abiding agent’s behavior. We experimentally validate our approach and show that our framework can successfully learn the most likely constraints that the agent respects. We further show that these learned constraints are \textit{transferable} to new agents that may have different morphologies and/or reward functions. Previous works in this regard have either mainly been restricted to tabular (discrete) settings, specific types of constraints or assume the environment’s transition dynamics. In contrast, our framework is able to learn arbitrary \textit{Markovian} constraints in high-dimensions in a completely model-free setting. The code is available at: \url{https://github.com/shehryar-malik/icrl}.

Fault diagnosis in industrial facilities has traditionally been done using rule-based approaches, heuristics or expert-knowledge. Bayesian network provides a flexible and data-driven alternative that can reason under uncertainty. Most of the data being generated by sensors in industrial setups are continuous and the underlying data-generating models are essentially non-linear. This paper employs Bayesian network and proposes a framework that learns parameters of probability density functions of a continuous Bayesian network using neural network/s without requiring assumption of linear Gaussian model or discretization of continuous data. Moreover, an expression of probability query using learned parametric density functions and causal-inference based mathematical formulation of two tasks related to fault diagnosis –in the context of industrial plants– namely root-cause-analysis and identification of most-influential-path in Bayesian network have been provided.

Trained generative models have shown remarkable performance as priors for inverse problems in imaging – for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training dataset. In this paper, we demonstrate that invertible neural networks, which have zero representation error by design, can be effective natural signal priors at inverse problems such as denoising, compressive sensing, and inpainting. Given a trained generative model, we study the empirical risk formulation of the desired inverse problem under a regularization that promotes high likelihood images, either directly by penalization or algorithmically by initialization. For compressive sensing, invertible priors can yield higher accuracy than sparsity priors across almost all undersampling ratios, and due to their lack of representation error, invertible priors can yield better reconstructions than GAN priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images. We additionally compare performance for compressive sensing to unlearned methods, such as the deep decoder, and we establish theoretical bounds on expected recovery error in the case of a linear invertible model.

We propose several sampling architectures for the efficient acquisition of an ensemble of correlated signals. We show that without prior knowledge of the correlation structure, each of our architectures (under different sets of assumptions) can acquire the ensemble at a sub-Nyquist rate. Prior to sampling, the analog signals are diversified using simple, implementable components. The diversification is achieved by injecting types of “structured randomness” into the ensemble, the result of which is subsampled. For reconstruction, the ensemble is modeled as a low-rank matrix that we have observed through an (undetermined) set of linear equations. Our main results show that this matrix can be recovered using a convex program when the total number of samples is on the order of the intrinsic degree of freedom of the ensemble - the more heavily correlated the ensemble, the fewer samples are needed. To motivate this study, we discuss how such ensembles arise in the context of array processing.

This paper shows that modulation protects a bandlimited signal against convolutive interference. A signal s(t), bandlimited to BHz, is modulated (pointwise multiplied) with a known random sign sequence r(t), alternating at a rate Q, and the resultant spread spectrum signal s(t) ⊙ r(t) is convolved against an M-tap channel impulse response h(t) to yield the observed signal y(t) = (s(t) ⊙ r(t)) ⊗ h(t), where ⊙ and ⊗ denote pointwise multiplication, and circular convolution, respectively.We show that both s(t), and h(t) can be provably recovered using a simple gradient descent scheme by alternating the binary waveform r(t) at a rate Q ≳ B + M(to within log factors and a signal coherences) and sampling y(t) at a rate Q. We also present a comprehensive set of phase transitions to depict the trade-off between Q, M, and B for successful recovery. Moreover, we show stable recovery results under noise.

This paper proposes a novel framework to regularize the highly ill-posed and non-linear Fourier ptychography problem using generative models. We demonstrate experimentally that our proposed algorithm, Deep Ptych, outperforms the existing Fourier ptychography techniques, in terms of quality of reconstruction and robustness against noise, using far fewer samples. We further modify the proposed approach to allow the generative model to explore solutions outside the range, leading to improved performance.

We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows a non-trivial convex relaxation of the bilinear measurements from convolution. We prove that if the two signals belong to known random subspaces of dimensions $k$ and $n$, then they can be recovered up to the inherent scaling ambiguity with $m \gg (k+n) \log^2 m$ phaseless measurements. Our method provides the first theoretical recovery guarantee for this problem by a computationally efficient algorithm and does not require a solution estimate to be computed for initialization. Our proof is based on Rademacher complexity estimates. Additionally, we provide an alternating direction method of multipliers (ADMM) implementation and provide numerical experiments that verify the theory.

We consider the bilinear inverse problem of recovering two vectors, x in R^L and w in R^L, from their entrywise product. We consider the case where x and w have known signs and are sparse with respect to known dictionaries of size K and N, respectively. Here, K and N may be larger than, smaller than, or equal to L. We introduce L1-BranchHull, which is a convex program posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved. We study the case where x and w are S1- and S2-sparse with respect to a random dictionary, with the sparse vectors satisfying an effective sparsity condition, and present a recovery guarantee that depends on the number of measurements as L > Omega(S1+S2)(log(K+N))^2. Numerical experiments verify that the scaling constant in the theorem is not too large. One application of this problem is the sweep distortion removal task in dielectric imaging, where one of the signals is a nonnegative reflectivity, and the other signal lives in a known subspace, for example that given by dominant wavelet coefficients. We also introduce a variants of L1-BranchHull for the purposes of tolerating noise and outliers, and for the purpose of recovering piecewise constant signals. We provide an ADMM implementation of these variants and show they can extract piecewise constant behavior from real images.

We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows a nontrivial convex relaxation of the bilinear measurements from convolution. We prove that if the two signals belong to known random subspaces of dimensions $k$ and $n$, then they can be recovered up to the inherent scaling ambiguity with $m >> (k+n) \log^2 m$ phaseless measurements. Our method provides the first theoretical recovery guarantee for this problem by a computationally efficient algorithm and does not require a solution estimate to be computed for initialization. Our proof is based Rademacher complexity estimates. Additionally, we provide an ADMM implementation of the method and provide numerical experiments that verify the theory.

This paper considers recovering L-dimensional vectors w, and x1, x2,⋯, xNfrom their circular convolutions yn= w*xn, n = 1, 2, 3,⋯, N. The vector w is assumed to be S-sparse in a known basis that is spread out in the Fourier domain, and each input xn is a member of a known K-dimensional random subspace. We prove that whenever K+S log2S ≲ L/ log4(LN), the problem can be solved effectively by using only the nuclear-norm minimization as the convex relaxation, as long as the inputs are sufficiently diverse and obey N ≳ log2(LN). By “diverse inputs,” we mean that the xn's belong to different, generic subspaces. To the best of our knowledge, this is the first theoretical result on blind deconvolution where the subspace to which w belongs is not fixed but needs to be determined. We discuss the result in the context of multipath channel estimation in wireless communications. Both the fading coefficients and the delays in the channel impulse response w are unknown. The encoder codes the K-dimensional message vectors randomly and then transmits coded messages xn's over a fixed channel one after the other. The decoder then discovers all of the messages and the channel response when the number of samples taken for each received message are roughly greater than (K + S log2S) log4(LN), and the number of messages is roughly at least log2(LN).

In this note we present our preliminary results relating the potential of data mining and machine learning techniques in educational setup of Pakistan. Our aim is to discover meaningful and insightful patterns out of the unstructured data collected during the monitoring process of these schools. After applying data science and machine learning techniques on Alif Ailaan district based school dataset of Pakistan we have shown that very useful latent performance metrics can be unveiled. We have highlighted important future directions and their potential of helping policy makers in making effective policies thus increasing the efficiency of the current educational infrastructure in Pakistan.

This letter presents a framework for the compressive acquisition of correlated signals. We propose an implementable sampling architecture for the acquisition of ensembles of correlated (lying in an a priori unknown subspace) signals at a sub-Nyquist rate. The sampling architecture acquires structured compressive samples of the signals after preprocessing them with easy-toimplement components. Quantitatively, we show that an ensemble of M correlated signals each of which is bandlimited to W/2 and can be decomposed as the linear combination of R underlying signals can be acquired at roughly RW (assuming without loss of generality M <; W ) samples per second. In the case, when M ≫ R, this results in significant reduction in the sampling rate compared to MW samples per second dictated by the Shannon-Nyquist sampling theorem. The signal reconstruction is achieved by solving only a least-squares program, which is in stark contrast to the prohibitively computationally expensive semidefinite programming techniques suggested in the earlier literature. We also provide rigorous analytical results to support our claims.

We present a general architecture for the acquisition of ensembles of correlated signals. The signals are multiplexed onto a single line by mixing each one against a different code and then adding them together, and the resulting signal is sampled at a high rate. We show that if the M signals, each band limited to W/2 Hz, can be approximated by a superposition of R <; M underlying signals, then the ensemble can be recovered by sampling at a rate within a logarithmic factor of RW, as compared with the cumulative Nyquist rate of MW. This sampling theorem shows that the correlation structure of the signal ensemble can be exploited in the acquisition process even though it is unknown a priori. The reconstruction of the ensemble is recast as a low-rank matrix recovery problem from linear measurements. The architectures we are considering impose a certain type of structure on the linear operators. Although our results depend on the mixing forms being random, this imposed structure results in a very different type of random projection than those analyzed in the low-rank recovery literature to date.

We consider the problem of recovering two unknown vectors, w and x, of length L from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with dimension N and the other with dimension K. Although the observed convolution is nonlinear in both w and x, it is linear in the rank-1 matrix formed by their outer product wx*. This observation allows us to recast the deconvolution problem as low-rank matrix recovery problem from linear measurements, whose natural convex relaxation is a nuclear norm minimization program. We prove the effectiveness of this relaxation by showing that, for “generic” signals, the program can deconvolve w and x exactly when the maximum of N and K is almost on the order of L. That is, we show that if x is drawn from a random subspace of dimension N, and w is a vector in a subspace of dimension K whose basis vectors are spread out in the frequency domain, then nuclear norm minimization recovers wx* without error. We discuss this result in the context of blind channel estimation in communications. If we have a message of length N, which we code using a random L x N coding matrix, and the encoded message travels through an unknown linear time-invariant channel of maximum length K, then the receiver can recover both the channel response and the message when L ≳ N + K, to within constant and log factors.

Recommendation systems are becoming increasingly important, as evidenced by the popularity of the Netflix prize and the sophistication of various online shopping systems. With this increase in interest, a new problem of nefarious or false rankings that compromise a recommendation system's integrity has surfaced. We consider such purposefully erroneous rankings to be a form of “toxic waste,” corrupting the performance of the underlying algorithm. In this paper, we propose an adaptive reweighted algorithm as a possible approach towards correcting this problem. Our algorithm relies on finding a low-rank-plus-sparse decomposition of the recommendation matrix, where the adaptation of the weights aids in rejecting the malicious contributions. Simulations suggest that our algorithm converges fairly rapidly and produces accurate results.