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Kernel methods are learning algorithms that enjoy solid theoretical foundations while suffering from important computational limitations. Sketching, that consists in looking for solutions among a subspace of reduced dimension, is a widely studied approach to alleviate this numerical burden. However, fast sketching strategies, such as non-adaptive subsampling, significantly degrade the guarantees of the algorithms, while theoretically-accurate sketches, such as the Gaussian one, turn out to remain relatively slow in practice. In this paper, we introduce the $p$-sparsified sketches, that combine the benefits from both approaches to achieve a good tradeoff between statistical accuracy and computational efficiency. To support our method, we derive excess risk bounds for both single and multiple output problems, with generic Lipschitz losses, providing new guarantees for a wide range of applications, from robust regression to multiple quantile regression. We also provide empirical evidences of the superiority of our sketches over recent SOTA approaches.

The seminal paper by Mazumdar and Saha \cite{MS17a} introduced an extensive line of work on clustering with noisy queries. Yet, despite significant progress on the problem, the proposed methods depend crucially on knowing the exact probabilities of errors of the underlying fully-random oracle. In this work, we develop robust learning methods that tolerate general semi-random noise obtaining qualitatively the same guarantees as the best possible methods in the fully-random model. More specifically, given a set of $n$ points with an unknown underlying partition, we are allowed to query pairs of points $u,v$ to check if they are in the same cluster, but with probability $p$, the answer may be adversarially chosen. We show that information theoretically $O\left(\frac{nk \log n} {(1-2p)^2}\right)$ queries suffice to learn any cluster of sufficiently large size. Our main result is a computationally efficient algorithm that can identify large clusters with $O\left(\frac{nk \log n} {(1-2p)^2}\right) + \text{poly}\left(\log n, k, \frac{1}{1-2p} \right)$ queries, matching the guarantees of the best known algorithms in the fully-random model. As a corollary of our approach, we develop the first parameter-free algorithm for the fully-random model, answering an open question by \cite{MS17a}.

We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established analytically.

The max-relative entropy and the conditional min-entropy it induces have become central to one-shot information theory. Both may be expressed in terms of a conic program over the positive semidefinite cone. Recently, it was shown that the same conic program altered to be over the separable cone admits an operational interpretation in terms of communicating classical information over a quantum channel. In this work, we generalize this framework of replacing the cone to determine which results in quantum information theory rely upon the positive semidefinite cone and which can be generalized. We show the fully quantum Stein's lemma and asymptotic equipartition property break down if the cone exponentially increases in resourcefulness but never approximates the positive semidefinite cone. However, we show for CQ states, the separable cone is sufficient to recover the asymptotic theory, thereby drawing a strong distinction between the fully and partial quantum settings. We present parallel results for the extended conditional min-entropy. In doing so, we extend the notion of k-superpositive channels to superchannels. We also present operational uses of this framework. We first show the cone restricted min-entropy of a Choi operator captures a measure of entanglement-assisted noiseless classical communication using restricted measurements. We show that quantum majorization results naturally generalize to other cones. As a novel example, we introduce a new min-entropy-like quantity that captures the quantum majorization of quantum channels in terms of bistochastic pre-processing. Lastly, we relate this framework to general conic norms and their non-additivity. Throughout this work we emphasize the introduced measures' relationship to general convex resource theories. In particular, we look at both resource theories that capture locality and resource theories of coherence/Abelian symmetries.

For the first time proposed: a method for representing the projections of a graph in computer memory and a description based on it of a quick search for shortest paths in unweighted dynamic graphs. The spatial complexity of the projection description does not exceed $(d + 1)\times n$ words, where $d$ is the diameter and $n$ is the number of vertices of the graph. The temporal difficulty of finding one shortest path between two vertices does not exceed d steps with the duration of elementary time of sampling a machine word. The solution can be applied in time delay-critical routing protocols of computer networks and supercomputers.

This paper focuses on improving the resource allocation algorithm in terms of packet delivery ratio (PDR), i.e., the number of successfully received packets sent by end devices (EDs) in a long-range wide-area network (LoRaWAN). Setting the transmission parameters significantly affects the PDR. Employing reinforcement learning (RL), we propose a resource allocation algorithm that enables the EDs to configure their transmission parameters in a distributed manner. We model the resource allocation problem as a multi-armed bandit (MAB) and then address it by proposing a two-phase algorithm named MIX-MAB, which consists of the exponential weights for exploration and exploitation (EXP3) and successive elimination (SE) algorithms. We evaluate the MIX-MAB performance through simulation results and compare it with other existing approaches. Numerical results show that the proposed solution performs better than the existing schemes in terms of convergence time and PDR.

Depth maps are used in a wide range of applications from 3D rendering to 2D image effects such as Bokeh. However, those predicted by single image depth estimation (SIDE) models often fail to capture isolated holes in objects and/or have inaccurate boundary regions. Meanwhile, high-quality masks are much easier to obtain, using commercial auto-masking tools or off-the-shelf methods of segmentation and matting or even by manual editing. Hence, in this paper, we formulate a novel problem of mask-guided depth refinement that utilizes a generic mask to refine the depth prediction of SIDE models. Our framework performs layered refinement and inpainting/outpainting, decomposing the depth map into two separate layers signified by the mask and the inverse mask. As datasets with both depth and mask annotations are scarce, we propose a self-supervised learning scheme that uses arbitrary masks and RGB-D datasets. We empirically show that our method is robust to different types of masks and initial depth predictions, accurately refining depth values in inner and outer mask boundary regions. We further analyze our model with an ablation study and demonstrate results on real applications. More information can be found at //sooyekim.github.io/MaskDepth/ .

It is a common paradigm in object detection frameworks to treat all samples equally and target at maximizing the performance on average. In this work, we revisit this paradigm through a careful study on how different samples contribute to the overall performance measured in terms of mAP. Our study suggests that the samples in each mini-batch are neither independent nor equally important, and therefore a better classifier on average does not necessarily mean higher mAP. Motivated by this study, we propose the notion of Prime Samples, those that play a key role in driving the detection performance. We further develop a simple yet effective sampling and learning strategy called PrIme Sample Attention (PISA) that directs the focus of the training process towards such samples. Our experiments demonstrate that it is often more effective to focus on prime samples than hard samples when training a detector. Particularly, On the MSCOCO dataset, PISA outperforms the random sampling baseline and hard mining schemes, e.g. OHEM and Focal Loss, consistently by more than 1% on both single-stage and two-stage detectors, with a strong backbone ResNeXt-101.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.

In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.