OpenRaiser/Intern-Atlas huggingface dataset:
Contingent Payment Mechanisms for Resource Utilization
Venue: arXiv cs.GT 2018
Year: 2018

We introduce the problem of assigning resources to improve their utilization. The motivation comes from settings where agents have uncertainty about their own values for using a resource, and where it is in the interest of a group that resources be used and not wasted. Done in the right way, improved utilization maximizes social welfare--- balancing the utility of a high value but unreliable agent with the group's preference that resources be used. We introduce the family of contingent payment mechanisms (CP), which may charge an agent contingent on use (a penalty). A CP mechanism is parameterized by a maximum penalty, and has a dominant-strategy equilibrium. Under a set of axiomatic properties, we establish welfare-optimality for the special case CP(W), with CP instantiated for a maximum penalty equal to societal value W for utilization. CP(W) is not dominated for expected welfare by any other mechanism, and second, amongst mechanisms that always allocate the resource and have a simple indirect structure, CP(W) strictly dominates every other mechanism. The special case with no upper bound on penalty, the contingent second-price mechanism, maximizes utilization. We extend the mechanisms to assign multiple, heterogeneous resources, and present a simulation study of the welfare properties of these mechanisms.
On the Resistance of Nearest Neighbor to Random Noisy Labels
Venue: arXiv cs.LG 2018
Year: 2018

Nearest neighbor has always been one of the most appealing non-parametric approaches in machine learning, pattern recognition, computer vision, etc. Previous empirical studies partly shows that nearest neighbor is resistant to noise, yet there is a lack of deep analysis. This work presents the finite-sample and distribution-dependent bounds on the consistency of nearest neighbor in the random noise setting. The theoretical results show that, for asymmetric noises, k-nearest neighbor is robust enough to classify most data correctly, except for a handful of examples, whose labels are totally misled by random noises. For symmetric noises, however, k-nearest neighbor achieves the same consistent rate as that of noise-free setting, which verifies the resistance of k-nearest neighbor to random noisy labels. Motivated by the theoretical analysis, we propose the Robust k-Nearest Neighbor (RkNN) approach to deal with noisy labels. The basic idea is to make unilateral corrections to examples, whose labels are totally misled by random noises, and classify the others directly by utilizing the robustness of k-nearest neighbor. We verify the effectiveness of the proposed algorithm both theoretically and empirically.
Cognitive Science in the era of Artificial Intelligence: A roadmap for reverse-engineering the infant language-learner
Venue: arXiv cs.CL 2018
Year: 2018

During their first years of life, infants learn the language(s) of their environment at an amazing speed despite large cross cultural variations in amount and complexity of the available language input. Understanding this simple fact still escapes current cognitive and linguistic theories. Recently, spectacular progress in the engineering science, notably, machine learning and wearable technology, offer the promise of revolutionizing the study of cognitive development. Machine learning offers powerful learning algorithms that can achieve human-like performance on many linguistic tasks. Wearable sensors can capture vast amounts of data, which enable the reconstruction of the sensory experience of infants in their natural environment. The project of 'reverse engineering' language development, i.e., of building an effective system that mimics infant's achievements appears therefore to be within reach. Here, we analyze the conditions under which such a project can contribute to our scientific understanding of early language development. We argue that instead of defining a sub-problem or simplifying the data, computational models should address the full complexity of the learning situation, and take as input the raw sensory signals available to infants. This implies that (1) accessible but privacy-preserving repositories of home data be setup and widely shared, and (2) models be evaluated at different linguistic levels through a benchmark of psycholinguist tests that can be passed by machines and humans alike, (3) linguistically and psychologically plausible learning architectures be scaled up to real data using probabilistic/optimization principles from machine learning. We discuss the feasibility of this approach and present preliminary results.
A Polynomial-Time Deterministic Approach to the Traveling Salesperson Problem
Venue: arXiv cs.DS 2018
Year: 2018

We propose a new polynomial-time deterministic algorithm that produces an approximated solution for the traveling salesperson problem. The proposed algorithm ranks cities based on their priorities calculated using a power function of means and standard deviations of their distances from other cities and then connects the cities to their neighbors in the order of their priorities. When connecting a city, a neighbor is selected based on their neighbors' priorities calculated as another power function that additionally includes their distance from the focal city to be connected. This repeats until all the cities are connected into a single loop. The time complexity of the proposed algorithm is $O(n^2)$, where $n$ is the number of cities. Numerical evaluation shows that, despite its simplicity, the proposed algorithm produces shorter tours with less time complexity than other conventional tour construction heuristics. The proposed algorithm can be used by itself or as an initial tour generator for other more complex heuristic optimization algorithms.
Steerable Principal Components for Space-Frequency Localized Images
Venue: arXiv cs.CV 2018
Year: 2018

This paper describes a fast and accurate method for obtaining steerable principal components from a large dataset of images, assuming the images are well localized in space and frequency. The obtained steerable principal components are optimal for expanding the images in the dataset and all of their rotations. The method relies upon first expanding the images using a series of two-dimensional Prolate Spheroidal Wave Functions (PSWFs), where the expansion coefficients are evaluated using a specially designed numerical integration scheme. Then, the expansion coefficients are used to construct a rotationally-invariant covariance matrix which admits a block-diagonal structure, and the eigen-decomposition of its blocks provides us with the desired steerable principal components. The proposed method is shown to be faster then existing methods, while providing appropriate error bounds which guarantee its accuracy.
Minimax Lower Bounds on Dictionary Learning for Tensor Data
Venue: arXiv cs.IT 2018
Year: 2018

This paper provides fundamental limits on the sample complexity of estimating dictionaries for tensor data. The specific focus of this work is on $K$th-order tensor data and the case where the underlying dictionary can be expressed in terms of $K$ smaller dictionaries. It is assumed the data are generated by linear combinations of these structured dictionary atoms and observed through white Gaussian noise. This work first provides a general lower bound on the minimax risk of dictionary learning for such tensor data and then adapts the proof techniques for specialized results in the case of sparse and sparse-Gaussian linear combinations. The results suggest the sample complexity of dictionary learning for tensor data can be significantly lower than that for unstructured data: for unstructured data it scales linearly with the product of the dictionary dimensions, whereas for tensor-structured data the bound scales linearly with the sum of the product of the dimensions of the (smaller) component dictionaries. A partial converse is provided for the case of 2nd-order tensor data to show that the bounds in this paper can be tight. This involves developing an algorithm for learning highly-structured dictionaries from noisy tensor data. Finally, numerical experiments highlight the advantages associated with explicitly accounting for tensor data structure during dictionary learning.
Cyclical Multiple Access in UAV-Aided Communications: A Throughput-Delay Tradeoff
Venue: arXiv cs.IT 2018
Year: 2018

This letter studies a wireless system consisting of distributed ground terminals (GTs) communicating with an unmanned aerial vehicle (UAV) that serves as a mobile base station (BS). The UAV flies cyclically above the GTs at a fixed altitude, which results in a cyclical pattern of the strength of the UAV-GT channels. To exploit such periodic channel variations, we propose a new cyclical multiple access (CMA) scheme to schedule the communications between the UAV and GTs in a cyclical time-division manner based on the flying UAV's position. The time allocations to different GTs are optimized to maximize their minimum throughput. It is revealed that there is a fundamental tradeoff between throughput and access delay in the proposed CMA. Simulation results show significant throughput gains over the case of a static UAV BS in delay-tolerant applications.
Cycles and Intractability in a Large Class of Aggregation Rules
Venue: arXiv cs.GT 2018
Year: 2018

We introduce the $(j,k)$-Kemeny rule -- a generalization of Kemeny's voting rule that aggregates $j$-chotomous weak orders into a $k$-chotomous weak order. Special cases of $(j,k)$-Kemeny include approval voting, the mean rule and Borda mean rule, as well as the Borda count and plurality voting. Why, then, is the winner problem computationally tractable for each of these other rules, but intractable for Kemeny? We show that intractability of winner determination for the $(j,k)$-Kemeny rule first appears at the $j=3$, $k=3$ level. The proof rests on a reduction of max cut to a related problem on weighted tournaments, and reveals that computational complexity arises from the cyclic part in the fundamental decomposition of a weighted tournament into cyclic and cocyclic components. Thus the existence of majority cycles -- the engine driving both Arrow's impossibility theorem and the Gibbard-Satterthwaite theorem -- also serves as a source of computational complexity in social choice.
On semiring complexity of Schur polynomials
Venue: arXiv cs.CC 2018
Year: 2018

Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that when the number of variables is fixed, the semiring complexity of a Schur polynomial $s_λ$ is $O(log(λ_1))$; here $λ_1$ is the largest part of the partition $λ$.
Semantic Understanding of Scenes through the ADE20K Dataset
Venue: arXiv cs.CV 2018
Year: 2018

Scene parsing, or recognizing and segmenting objects and stuff in an image, is one of the key problems in computer vision. Despite the community's efforts in data collection, there are still few image datasets covering a wide range of scenes and object categories with dense and detailed annotations for scene parsing. In this paper, we introduce and analyze the ADE20K dataset, spanning diverse annotations of scenes, objects, parts of objects, and in some cases even parts of parts. A generic network design called Cascade Segmentation Module is then proposed to enable the segmentation networks to parse a scene into stuff, objects, and object parts in a cascade. We evaluate the proposed module integrated within two existing semantic segmentation networks, yielding significant improvements for scene parsing. We further show that the scene parsing networks trained on ADE20K can be applied to a wide variety of scenes and objects.
$χ$-bounds, operations and chords
Venue: arXiv cs.DM 2018
Year: 2018

A \emph{long unichord} in a graph is an edge that is the unique chord of some cycle of length at least 5. A graph is \emph{long-unichord-free} if it does not contain any long-unichord. We prove a structure theorem for long-unichord-free graph. We give an $O(n^4m)$-time algorithm to recognize them. We show that any long-unichord-free graph $G$ can be colored with at most $O(ω^3)$ colors, where $ω$ is the maximum number of pairwise adjacent vertices in $G$.
Skew-t Filter and Smoother with Improved Covariance Matrix Approximation
Venue: arXiv cs.SY 2018
Year: 2018

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness variables to reduce the error caused by the variational approximation. Although the variational update is done suboptimally using an expectation propagation algorithm, our simulations show that the proposed method gives a more accurate approximation of the posterior covariance matrix than an earlier proposed variational algorithm. Consequently, the novel filter and smoother outperform the earlier proposed robust filter and smoother and other existing low-complexity alternatives in accuracy and speed. We present both simulations and tests based on real-world navigation data, in particular GPS data in an urban area, to demonstrate the performance of the novel methods. Moreover, the extension of the proposed algorithms to cover the case where the distribution of the measurement noise is multivariate skew-$t$ is outlined. Finally, the paper presents a study of theoretical performance bounds for the proposed algorithms.
Random Forest for Label Ranking
Venue: arXiv cs.LG 2018
Year: 2018

Label ranking aims to learn a mapping from instances to rankings over a finite number of predefined labels. Random forest is a powerful and one of the most successful general-purpose machine learning algorithms of modern times. In this paper, we present a powerful random forest label ranking method which uses random decision trees to retrieve nearest neighbors. We have developed a novel two-step rank aggregation strategy to effectively aggregate neighboring rankings discovered by the random forest into a final predicted ranking. Compared with existing methods, the new random forest method has many advantages including its intrinsically scalable tree data structure, highly parallel-able computational architecture and much superior performance. We present extensive experimental results to demonstrate that our new method achieves the highly competitive performance compared with state-of-the-art methods for datasets with complete ranking and datasets with only partial ranking information.
Axiomatizing Category Theory in Free Logic
Venue: arXiv cs.LO 2018
Year: 2018

Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL interactive proof assistant, and this formalization utilizes a semantically correct embedding of free logic in classical higher-order logic. The modeling and formal analysis of our axiom sets has been significantly supported by series of experiments with automated reasoning tools integrated with Isabelle/HOL. We also address the relation of our axiom systems to alternative proposals from the literature, including an axiom set proposed by Freyd and Scedrov for which we reveal a technical issue (when encoded in free logic where free variables range over defined and undefined objects): either all operations, e.g. morphism composition, are total or their axiom system is inconsistent. The repair for this problem is quite straightforward, however.
A Boosting Method to Face Image Super-resolution
Venue: arXiv cs.CV 2018
Year: 2018

Recently sparse representation has gained great success in face image super-resolution. The conventional sparsity-based methods enforce sparse coding on face image patches and the representation fidelity is measured by $\ell_{2}$-norm. Such a sparse coding model regularizes all facial patches equally, which however ignores distinct natures of different facial patches for image reconstruction. In this paper, we propose a new weighted-patch super-resolution method based on AdaBoost. Specifically, in each iteration of the AdaBoost operation, each facial patch is weighted automatically according to the performance of the model on it, so as to highlight those patches that are more critical for improving the reconstruction power in next step. In this way, through the AdaBoost training procedure, we can focus more on the patches (face regions) with richer information. Various experimental results on standard face database show that our proposed method outperforms state-of-the-art methods in terms of both objective metrics and visual quality.
Paraunitary Matrices, Entropy, Algebraic Condition Number and Fourier Computation
Venue: arXiv cs.CC 2018
Year: 2018

The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. From a lower bound perspective, relatively little is known. Ailon shows in 2013 an $Ω(n\log n)$ bound for computing the normalized Fourier Transform assuming only unitary operations on two coordinates are allowed at each step, and no extra memory is allowed. In 2014, Ailon then improved the result to show that, in a $κ$-well conditioned computation, Fourier computation can be sped up by no more than $O(κ)$. The main conjecture is that Ailon's result can be exponentially improved, in the sense that $κ$-well condition cannot admit $ω(\log κ)$ speedup. The main result here is that `algebraic' $κ$-well condition admits no more than $O(\sqrt κ)$ speedup. The definition of algebraic condition number is obtained by formally viewing multiplication by constants, as performed by the algorithm, as multiplication by indeterminates, giving rise to computation over polynomials. The algebraic condition number is related to the degree of these polynomials. Using the maximum modulus theorem from complex analysis, we show that algebraic condition number upper bounds standard condition number, and equals it in certain cases. Algebraic condition number is an interesting measure of numerical computation stability in its own right. Moreover, we believe that the approach of algebraic condition number has a good chance of establishing an algebraic version of the main conjecture.
Bounds on Separating Redundancy of Linear Codes and Rates of X-Codes
Venue: arXiv cs.IT 2018
Year: 2018

An error-erasure channel is a simple noise model that introduces both errors and erasures. While the two types of errors can be corrected simultaneously with error-correcting codes, it is also known that any linear code allows for first correcting errors and then erasures in two-step decoding. In particular, a carefully designed parity-check matrix not only allows for separating erasures from errors but also makes it possible to efficiently correct erasures. The separating redundancy of a linear code is the number of parity-check equations in a smallest parity-check matrix that has the required property for this error-erasure separation. In a sense, it is a parameter of a linear code that represents the minimum overhead for efficiently separating erasures from errors. While several bounds on separating redundancy are known, there still remains a wide gap between upper and lower bounds except for a few limited cases. In this paper, using probabilistic combinatorics and design theory, we improve both upper and lower bounds on separating redundancy. We also show a relation between parity-check matrices for error-erasure separation and special matrices, called X-codes, for data compaction circuits in VLSI testing. This leads to an exponentially improved bound on the size of an optimal X-code.
A Distributed Observer for a Time-Invariant Linear System
Venue: arXiv cs.SY 2018
Year: 2018

A time-invariant, linear, distributed observer is described for estimating the state of an $m>0$ channel, $n$-dimensional continuous-time linear system of the form $ \dot{x} = Ax,\ y_i = C_i x,\ i \in \{1,2,\cdots, m\}$. The state $x$ is simultaneously estimated by $m$ agents assuming each agent $i$ senses $y_i$ and receives the state $z_j$ of each of its neighbors' estimators. Neighbor relations are characterized by a constant directed graph $\mathbb{N}$ whose vertices correspond to agents and whose arcs depict neighbor relations. The overall distributed observer consists of $m$ linear estimators, one for each agent; $m-1$ of the estimators are of dimension $n$ and one estimator is of dimension $n+m-1$. Using results from classical decentralized control theory, it is shown that subject to the assumptions that (i) none of the $C_i$ are zero, (ii) the neighbor graph $\mathbb{N}$ is strongly connected, (iii) the system whose state is to be estimated is jointly observable, and nothing more, it is possible to freely assign the spectrum of the overall distributed observer.
QUARKS: Identification of large-scale Kronecker Vector-AutoRegressive models
Venue: arXiv cs.SY 2018
Year: 2018

In this paper we propose a Kronecker-based modeling for identifying the spatial-temporal dynamics of large sensor arrays. The class of Kronecker networks is defined for which we formulate a Vector Autoregressive model. Its coefficient-matrices are decomposed into a sum of Kronecker products. For a two-dimensional array of size $N \times N$, and when the number of terms in the sum is small compared to $N$, exploiting the Kronecker structure leads to high data compression. We propose an Alternating Least Squares algorithm to identify the coefficient matrices with $\mathcal{O}(N^3N_t)$, where $N_t$ is the number of temporal samples, instead of $\mathcal{O}(N^6)$ in the unstructured case. This framework moreover allows for a convenient integration of more structure (e.g sparse, banded, Toeplitz) on the factor matrices. Numerical examples on atmospheric turbulence data has shown comparable performances with the unstructured least-squares estimation while the number of parameters is growing only linearly w.r.t. the number of nodes instead of quadratically in the full unstructured matrix case.
Function Computation through a Bidirectional Relay
Venue: arXiv cs.IT 2018
Year: 2018

We consider a function computation problem in a three node wireless network. Nodes A and B observe two correlated sources $X$ and $Y$ respectively, and want to compute a function $f(X,Y)$. To achieve this, nodes A and B send messages to a relay node C at rates $R_A$ and $R_B$ respectively. The relay C then broadcasts a message to A and B at rate $R_C$. We allow block coding, and study the achievable region of rate triples under both zero-error and $ε$-error. As a preparation, we first consider a broadcast network from the relay to A and B. A and B have side information $X$ and $Y$ respectively. The relay node C observes both $X$ and $Y$ and broadcasts an encoded message to A and B. We want to obtain the optimal broadcast rate such that A and B can recover the function $f(X,Y)$ from the received message and their individual side information $X$ and $Y$ respectively. For this problem, we show equivalence between $ε$-error and zero-error computations-- this gives a rate characterization for zero-error computation. As a corollary, this also gives a rate characterization for the relay network under zero-error for a class of functions called {\em component-wise one-to-one functions} when the support set of $p_{XY}$ is full. For the relay network, the zero-error rate region for arbitrary functions is characterized in terms of graph coloring of some suitably defined probabilistic graphs. We then give a single-letter inner bound to this rate region. Further, we extend the graph theoretic ideas to address the $ε$-error problem and obtain a single-letter inner bound.