Recent advances in methods focused on the grounding problem have resulted in techniques that can be used to construct a symbolic language associated with a specific domain. Inspired by how humans communicate complex ideas through language, we developed a generalized Symbolic Semantic ($\text{S}^2$) framework for interpretable segmentation. Unlike adversarial models (e.g., GANs), we explicitly model cooperation between two agents, a Sender and a Receiver, that must cooperate to achieve a common goal. The Sender receives information from a high layer of a segmentation network and generates a symbolic sentence derived from a categorical distribution. The Receiver obtains the symbolic sentences and co-generates the segmentation mask. In order for the model to converge, the Sender and Receiver must learn to communicate using a private language. We apply our architecture to segment tumors in the TCGA dataset. A UNet-like architecture is used to generate input to the Sender network which produces a symbolic sentence, and a Receiver network co-generates the segmentation mask based on the sentence. Our Segmentation framework achieved similar or better performance compared with state-of-the-art segmentation methods. In addition, our results suggest direct interpretation of the symbolic sentences to discriminate between normal and tumor tissue, tumor morphology, and other image characteristics.

We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations (a.k.a. blind deconvolution under a subspace model). Despite the wide applicability, the theoretical understanding about these two paradigms remains largely inadequate in the presence of noise. The current paper makes two contributions by demonstrating that: (1) convex relaxation achieves minimax-optimal statistical accuracy vis-\`a-vis random noise, and (2) a two-stage nonconvex algorithm attains minimax-optimal accuracy within a logarithmic number of iterations. Both results improve upon the state-of-the-art results by some factors that scale polynomially in the problem dimension.

Following the recent enthusiasm for Machine Learning (ML) methods and widespread availability of big data, macroeconomic forecasting research gradually evolved further and further away from the traditional tightly specified OLS regression. Rather, nonparametric non-linearity and regularization of many forms are slowly taking the center stage, largely because they can provide sizable forecasting gains with respect to traditional methods (see, among others, Kim and Swanson (2018); Medeiros et al. (2019); Goulet Coulombe et al. (2020); Goulet Coulombe (2020a)). In such environments, different linear transformations of the informational set X can change the prediction and taking first differences may not be the optimal transformation for many predictors, despite the fact that it guarantees viable frequentist inference. For instance, in penalized regression problems - like Lasso or Ridge, different rotations of X imply different priors on β in the original regressor space.

Space-filling curves like the Hilbert-curve, Peano-curve and Z-order map natural or real numbers from a two or higher dimensional space to a one dimensional space preserving locality. They have numerous applications like search structures, computer graphics, numerical simulation, cryptographics and can be used to make various algorithms cache-oblivious. In this paper, we describe some details of the Hilbert-curve. We define the Hilbert-curve in terms of a finite automaton of Mealy-type which determines from the two-dimensional coordinate space the Hilbert order value and vice versa in a logarithmic number of steps. And we define a context-free grammar to generate the whole curve in a time which is linear in the number of generated coordinate/order value pairs, i.e. a constant time per coordinate pair or order value. We also review two different strategies which enable the generation of curves without the usual restriction to square-like grids where the side-length is a power of two. Finally, we elaborate on a few applications, namely matrix multiplication, Cholesky decomposition, the Floyd-Warshall algorithm, k-Means clustering, and the similarity join.

Classical iterative algorithms for linear system solving and regression are brittle to the condition number of the data matrix. Even a semi-random adversary, constrained to only give additional consistent information, can arbitrarily hinder the resulting computational guarantees of existing solvers. We show how to overcome this barrier by developing a framework which takes state-of-the-art solvers and "robustifies" them to achieve comparable guarantees against a semi-random adversary. Given a matrix which contains an (unknown) well-conditioned submatrix, our methods obtain computational and statistical guarantees as if the entire matrix was well-conditioned. We complement our theoretical results with preliminary experimental evidence, showing that our methods are effective in practice.

Due to its low storage cost and fast query speed, hashing has been widely used in large-scale image retrieval tasks. Hash bucket search returns data points within a given Hamming radius to each query, which can enable search at a constant or sub-linear time cost. However, existing hashing methods cannot achieve satisfactory retrieval performance for hash bucket search in complex scenarios, since they learn only one hash code for each image. More specifically, by using one hash code to represent one image, existing methods might fail to put similar image pairs to the buckets with a small Hamming distance to the query when the semantic information of images is complex. As a result, a large number of hash buckets need to be visited for retrieving similar images, based on the learned codes. This will deteriorate the efficiency of hash bucket search. In this paper, we propose a novel hashing framework, called multiple code hashing (MCH), to improve the performance of hash bucket search. The main idea of MCH is to learn multiple hash codes for each image, with each code representing a different region of the image. Furthermore, we propose a deep reinforcement learning algorithm to learn the parameters in MCH. To the best of our knowledge, this is the first work that proposes to learn multiple hash codes for each image in image retrieval. Experiments demonstrate that MCH can achieve a significant improvement in hash bucket search, compared with existing methods that learn only one hash code for each image.

In this paper, we show that, in vector-to-vector regression utilizing deep neural networks (DNNs), a generalized loss of mean absolute error (MAE) between the predicted and expected feature vectors is upper bounded by the sum of an approximation error, an estimation error, and an optimization error. Leveraging upon error decomposition techniques in statistical learning theory and non-convex optimization theory, we derive upper bounds for each of the three aforementioned errors and impose necessary constraints on DNN models. Moreover, we assess our theoretical results through a set of image de-noising and speech enhancement experiments. Our proposed upper bounds of MAE for DNN based vector-to-vector regression are corroborated by the experimental results and the upper bounds are valid with and without the "over-parametrization" technique.

We present an end-to-end, interpretable, deep-learning architecture to learn a graph kernel that predicts the outcome of chronic disease drug prescription. This is achieved through a deep metric learning collaborative with a Support Vector Machine objective using a graphical representation of Electronic Health Records. We formulate the predictive model as a binary graph classification problem with an adaptive learned graph kernel through novel cross-global attention node matching between patient graphs, simultaneously computing on multiple graphs without training pair or triplet generation. Results using the Taiwanese National Health Insurance Research Database demonstrate that our approach outperforms current start-of-the-art models both in terms of accuracy and interpretability.

This article considers "sketched learning," or "compressive learning," an approach to large-scale machine learning where datasets are massively compressed before learning (e.g., clustering, classification, or regression) is performed. In particular, a "sketch" is first constructed by computing carefully chosen nonlinear random features (e.g., random Fourier features) and averaging them over the whole dataset. Parameters are then learned from the sketch, without access to the original dataset. This article surveys the current state-of-the-art in sketched learning, including the main concepts and algorithms, their connections with established signal-processing methods, existing theoretical guarantees---on both information preservation and privacy preservation, and important open problems.

The classical Perceptron algorithm provides a simple and elegant procedure for learning a linear classifier. In each step, the algorithm observes the sample's position and label and may update the current predictor accordingly. In presence of strategic agents, however, the classifier may not be able to observe the true position but a position where the agent pretends to be in order to be classified desirably. Unlike the original setting with perfect knowledge of positions, in this situation the Perceptron algorithm fails to achieve its guarantees, and we illustrate examples with the predictor oscillating between two solutions forever, never reaching a perfect classifier even though one exists. Our main contribution is providing a modified Perceptron-style algorithm which finds a classifier in presence of strategic agents with both $\ell_2$ and weighted $\ell_1$ manipulation costs. In our baseline model, knowledge of the manipulation costs is assumed. In our most general model, we relax this assumption and provide an algorithm which learns and refines both the classifier and its cost estimates to achieve good mistake bounds even when manipulation costs are unknown.