The channel synthesis problem has been widely investigated over the last decade. In this paper, we consider the sequential version in which the encoder and the decoder work in a sequential way. Under a mild assumption on the target joint distribution we provide a complete (single-letter) characterization of the solution for the point-to-point case, which shows that the canonical symbol-by-symbol mapping is not optimal in general, but is indeed optimal if we make some additional assumptions on the encoder and decoder. We also extend this result to the broadcast scenario and the interactive communication scenario. We provide bounds in the broadcast setting and a complete characterization of the solution under a mild condition on the target joint distribution in the interactive communication case. Our proofs are based on a R\'enyi entropy method.
相關內容
Given its status as a classic problem and its importance to both theoreticians and practitioners, edit distance provides an excellent lens through which to understand how the theoretical analysis of algorithms impacts practical implementations. From an applied perspective, the goals of theoretical analysis are to predict the empirical performance of an algorithm and to serve as a yardstick to design novel algorithms that perform well in practice. In this paper, we systematically survey the types of theoretical analysis techniques that have been applied to edit distance and evaluate the extent to which each one has achieved these two goals. These techniques include traditional worst-case analysis, worst-case analysis parametrized by edit distance or entropy or compressibility, average-case analysis, semi-random models, and advice-based models. We find that the track record is mixed. On one hand, two algorithms widely used in practice have been born out of theoretical analysis and their empirical performance is captured well by theoretical predictions. On the other hand, all the algorithms developed using theoretical analysis as a yardstick since then have not had any practical relevance. We conclude by discussing the remaining open problems and how they can be tackled.
Optimal feedback control (OFC) is a theory from the motor control literature that explains how humans move their body to achieve a certain goal, e.g., pointing with the finger. OFC is based on the assumption that humans aim to control their body optimally, within the constraints imposed by body, environment, and task. In this paper, we explain how this theory can be applied to understanding Human-Computer Interaction (HCI) in the case of pointing. We propose that the human body and computer dynamics can be interpreted as a single dynamical system. The system state is controlled by the user via muscle control signals, and estimated from observations. Between-trial variability arises from signal-dependent control noise and observation noise. We compare four different models from optimal control theory and evaluate to what degree these models can replicate movements in the case of mouse pointing. We introduce a procedure to identify parameters that best explain observed user behavior. To support HCI researchers in simulating, analyzing, and optimizing interaction movements, we provide the Python toolbox OFC4HCI. We conclude that OFC presents a powerful framework for HCI to understand and simulate motion of the human body and of the interface on a moment by moment basis.
We consider the offline constrained reinforcement learning (RL) problem, in which the agent aims to compute a policy that maximizes expected return while satisfying given cost constraints, learning only from a pre-collected dataset. This problem setting is appealing in many real-world scenarios, where direct interaction with the environment is costly or risky, and where the resulting policy should comply with safety constraints. However, it is challenging to compute a policy that guarantees satisfying the cost constraints in the offline RL setting, since the off-policy evaluation inherently has an estimation error. In this paper, we present an offline constrained RL algorithm that optimizes the policy in the space of the stationary distribution. Our algorithm, COptiDICE, directly estimates the stationary distribution corrections of the optimal policy with respect to returns, while constraining the cost upper bound, with the goal of yielding a cost-conservative policy for actual constraint satisfaction. Experimental results show that COptiDICE attains better policies in terms of constraint satisfaction and return-maximization, outperforming baseline algorithms.
We consider the question of adaptive data analysis within the framework of convex optimization. We ask how many samples are needed in order to compute $\epsilon$-accurate estimates of $O(1/\epsilon^2)$ gradients queried by gradient descent, and we provide two intermediate answers to this question. First, we show that for a general analyst (not necessarily gradient descent) $\Omega(1/\epsilon^3)$ samples are required. This rules out the possibility of a foolproof mechanism. Our construction builds upon a new lower bound (that may be of interest of its own right) for an analyst that may ask several non adaptive questions in a batch of fixed and known $T$ rounds of adaptivity and requires a fraction of true discoveries. We show that for such an analyst $\Omega (\sqrt{T}/\epsilon^2)$ samples are necessary. Second, we show that, under certain assumptions on the oracle, in an interaction with gradient descent $\tilde \Omega(1/\epsilon^{2.5})$ samples are necessary. Our assumptions are that the oracle has only \emph{first order access} and is \emph{post-hoc generalizing}. First order access means that it can only compute the gradients of the sampled function at points queried by the algorithm. Our assumption of \emph{post-hoc generalization} follows from existing lower bounds for statistical queries. More generally then, we provide a generic reduction from the standard setting of statistical queries to the problem of estimating gradients queried by gradient descent. These results are in contrast with classical bounds that show that with $O(1/\epsilon^2)$ samples one can optimize the population risk to accuracy of $O(\epsilon)$ but, as it turns out, with spurious gradients.
We study the problem of testing whether a function $f: \mathbb{R}^n \to \mathbb{R}$ is a polynomial of degree at most $d$ in the \emph{distribution-free} testing model. Here, the distance between functions is measured with respect to an unknown distribution $\mathcal{D}$ over $\mathbb{R}^n$ from which we can draw samples. In contrast to previous work, we do not assume that $\mathcal{D}$ has finite support. We design a tester that given query access to $f$, and sample access to $\mathcal{D}$, makes $(d/\varepsilon)^{O(1)}$ many queries to $f$, accepts with probability $1$ if $f$ is a polynomial of degree $d$, and rejects with probability at least $2/3$ if every degree-$d$ polynomial $P$ disagrees with $f$ on a set of mass at least $\varepsilon$ with respect to $\mathcal{D}$. Our result also holds under mild assumptions when we receive only a polynomial number of bits of precision for each query to $f$, or when $f$ can only be queried on rational points representable using a logarithmic number of bits. Along the way, we prove a new stability theorem for multivariate polynomials that may be of independent interest.
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards a lower-dimensional subspace; the projection onto the subspace gives the low-dimensional embedding. Training the model involves identifying the nonlinear flow and the subspace. Following the equation discovery method, we represent the vector field that defines the flow using a linear combination of dictionary elements, where each element is a pre-specified linear/nonlinear candidate function. A regularization term for the average total kinetic energy is also introduced and motivated by optimal transport theory. We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method. We also show how the DDR method can be trained using a gradient-based optimization method, where the gradients are computed using the adjoint method from optimal control theory. The DDR method is implemented and compared on synthetic and example datasets to other dimension reductions methods, including PCA, t-SNE, and Umap.
The fact that the millimeter-wave (mmWave) multiple-input multiple-output (MIMO) channel has sparse support in the spatial domain has motivated recent compressed sensing (CS)-based mmWave channel estimation methods, where the angles of arrivals (AoAs) and angles of departures (AoDs) are quantized using angle dictionary matrices. However, the existing CS-based methods usually obtain the estimation result through one-stage channel sounding that have two limitations: (i) the requirement of large-dimensional dictionary and (ii) unresolvable quantization error. These two drawbacks are irreconcilable; improvement of the one implies deterioration of the other. To address these challenges, we propose, in this paper, a two-stage method to estimate the AoAs and AoDs of mmWave channels. In the proposed method, the channel estimation task is divided into two stages, Stage I and Stage II. Specifically, in Stage I, the AoAs are estimated by solving a multiple measurement vectors (MMV) problem. In Stage II, based on the estimated AoAs, the receive sounders are designed to estimate AoDs. The dimension of the angle dictionary in each stage can be reduced, which in turn reduces the computational complexity substantially. We then analyze the successful recovery probability (SRP) of the proposed method, revealing the superiority of the proposed framework over the existing one-stage CS-based methods. We further enhance the reconstruction performance by performing resource allocation between the two stages. We also overcome the unresolvable quantization error issue present in the prior techniques by applying the atomic norm minimization method to each stage of the proposed two-stage approach. The simulation results illustrate the substantially improved performance with low complexity of the proposed two-stage method.
The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used schemes to compute MEPs numerically. It approximates an MEP by a discrete set of configuration images, where the discretization size determines both computational cost and accuracy of the simulations. In this paper, we consider a discrete MEP to be a stationary state of the NEB method and prove an optimal convergence rate of the discrete MEP with respect to the number of images. Numerical simulations for the transitions of some several proto-typical model systems are performed to support the theory.
Deep Learning has implemented a wide range of applications and has become increasingly popular in recent years. The goal of multimodal deep learning is to create models that can process and link information using various modalities. Despite the extensive development made for unimodal learning, it still cannot cover all the aspects of human learning. Multimodal learning helps to understand and analyze better when various senses are engaged in the processing of information. This paper focuses on multiple types of modalities, i.e., image, video, text, audio, body gestures, facial expressions, and physiological signals. Detailed analysis of past and current baseline approaches and an in-depth study of recent advancements in multimodal deep learning applications has been provided. A fine-grained taxonomy of various multimodal deep learning applications is proposed, elaborating on different applications in more depth. Architectures and datasets used in these applications are also discussed, along with their evaluation metrics. Last, main issues are highlighted separately for each domain along with their possible future research directions.
This paper proposes a recommender system to alleviate the cold-start problem that can estimate user preferences based on only a small number of items. To identify a user's preference in the cold state, existing recommender systems, such as Netflix, initially provide items to a user; we call those items evidence candidates. Recommendations are then made based on the items selected by the user. Previous recommendation studies have two limitations: (1) the users who consumed a few items have poor recommendations and (2) inadequate evidence candidates are used to identify user preferences. We propose a meta-learning-based recommender system called MeLU to overcome these two limitations. From meta-learning, which can rapidly adopt new task with a few examples, MeLU can estimate new user's preferences with a few consumed items. In addition, we provide an evidence candidate selection strategy that determines distinguishing items for customized preference estimation. We validate MeLU with two benchmark datasets, and the proposed model reduces at least 5.92% mean absolute error than two comparative models on the datasets. We also conduct a user study experiment to verify the evidence selection strategy.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191