Iterative deepening search is used in applications where the best cost bound for state-space search is unknown. The iterative deepening process is used to avoid overshooting the appropriate cost bound and doing too much work as a result. However, iterative deepening search also does too much work if the cost bound grows too slowly. This paper proposes a new framework for iterative deepening search called exponential-binary state-space search. The approach interleaves exponential and binary searches to find the desired cost bound, reducing the worst-case overhead from polynomial to logarithmic. Exponential-binary search can be used with bounded depth-first search to improve the worst-case performance of IDA* and with breadth-first heuristic search to improve the worst-case performance of search with inconsistent heuristics.

Consider a discrete-time Markovian decision process (MDP) where a decision-maker (DM) interacts with a system iteratively: in each round, the DM first observes the current state of the system, and then picks an available action. Afterwards, it receives an instant random reward, and the system transits to the next state according to some state transition distribution. The reward distribution and the state transition distribution depend on the current state and the chosen action, but are independent of all the previous states and actions. The goal of the DM is to maximize its cumulative rewards under the following challenges: - Uncertainty: the reward and the state transition distributions are initially unknown to the DM. - Non-stationarity: the environment is non-stationary, and both of the reward distributions and the state transition distributions can evolve over time.

Optimal transport costs, which include the Wasserstein Distance and the Earth-Mover-Distance as special cases, have become useful tools in machine learning and statistics [16, 3, 1, 18, 8, 6]. The optimal transport cost between two distributions is computed (in its primal form) as a minimization problem, in which the cost of transporting one distribution to another is minimized over all possible joint distributions, leading to linear program (see for example,[26]). Optimal transport provides great flexibility when comparing (probability) measures and histograms. The transportation cost function (which we refer to as the cost function) can be used to capture key geometric characteristics [16]. It can be also used to compare discrete vs continuous distributions directly, without introducing smoothing, in contrast to alternatives such as the Kullback-Leibler divergence (see [3, 13] for more details). Also, by judiciously choosing the cost function, a Wasserstein distance can generate either the topology corresponding to weak convergence or the total variation distance. In data-driven applications, one needs to estimate the optimal transport cost by means of sampled data.

To provide more accurate, diverse, and explainable recommendation, it is compulsory to go beyond modeling user-item interactions and take side information into account. Traditional methods like factorization machine (FM) cast it as a supervised learning problem, which assumes each interaction as an independent instance with side information encoded. Due to the overlook of the relations among instances or items (e.g., the director of a movie is also an actor of another movie), these methods are insufficient to distill the collaborative signal from the collective behaviors of users. In this work, we investigate the utility of knowledge graph (KG), which breaks down the independent interaction assumption by linking items with their attributes. We argue that in such a hybrid structure of KG and user-item graph, high-order relations --- which connect two items with one or multiple linked attributes --- are an essential factor for successful recommendation. We propose a new method named Knowledge Graph Attention Network (KGAT) which explicitly models the high-order connectivities in KG in an end-to-end fashion. It recursively propagates the embeddings from a node's neighbors (which can be users, items, or attributes) to refine the node's embedding, and employs an attention mechanism to discriminate the importance of the neighbors. Our KGAT is conceptually advantageous to existing KG-based recommendation methods, which either exploit high-order relations by extracting paths or implicitly modeling them with regularization. Empirical results on three public benchmarks show that KGAT significantly outperforms state-of-the-art methods like Neural FM and RippleNet. Further studies verify the efficacy of embedding propagation for high-order relation modeling and the interpretability benefits brought by the attention mechanism.

We introduce and analyze two parameter-free linear-memory tree search algorithms. Under mild assumptions we prove our algorithms are guaranteed to perform only a logarithmic factor more node expansions than A* when the search space is a tree. Previously, the best guarantee for a linear-memory algorithm under similar assumptions was achieved by IDA*, which in the worst case expands quadratically more nodes than in its last iteration. Empirical results support the theory and demonstrate the practicality and robustness of our algorithms. Furthermore, they are fast and easy to implement.

Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this paper, we study transfer learning in the context of nonparametric classification based on observations from different distributions under the posterior drift model, which is a general framework and arises in many practical problems. We first establish the minimax rate of convergence and construct a rate-optimal two-sample weighted $K$-NN classifier. The results characterize precisely the contribution of the observations from the source distribution to the classification task under the target distribution. A data-driven adaptive classifier is then proposed and is shown to simultaneously attain within a logarithmic factor of the optimal rate over a large collection of parameter spaces. Simulation studies and real data applications are carried out where the numerical results further illustrate the theoretical analysis. Extensions to the case of multiple source distributions are also considered.

State-of-the art vision models can achieve superhuman performance on image classification tasks when testing and training data come from the same distribution. However, when models are tested on corrupted images (e.g. due to scale changes, translations, or shifts in brightness or contrast), performance degrades significantly. Here, we explore the possibility of meta-training a learned optimizer that can train image classification models such that they are robust to common image corruptions. Specifically, we are interested training models that are more robust to noise distributions not present in the training data. We find that a learned optimizer meta-trained to produce models which are robust to Gaussian noise trains models that are more robust to Gaussian noise at other scales compared to traditional optimizers like Adam. The effect of meta-training is more complicated when targeting a more general set of noise distributions, but led to improved performance on half of held-out corruption tasks. Our results suggest that meta-learning provides a novel approach for studying and improving the robustness of deep learning models.

We propose the use of a proportional-derivative (PD) control based policy learned via reinforcement learning (RL) to estimate and forecast 3D human pose from egocentric videos. The method learns directly from unsegmented egocentric videos and motion capture data consisting of various complex human motions (e.g., crouching, hopping, bending, and motion transitions). We propose a video-conditioned recurrent control technique to forecast physically-valid and stable future motions of arbitrary length. We also introduce a value function based fail-safe mechanism which enables our method to run as a single pass algorithm over the video data. Experiments with both controlled and in-the-wild data show that our approach outperforms previous art in both quantitative metrics and visual quality of the motions, and is also robust enough to transfer directly to real-world scenarios. Additionally, our time analysis shows that the combined use of our pose estimation and forecasting can run at 30 FPS, making it suitable for real-time applications.

Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The drawback to this approach is that GPFA priors are not conjugate to count model likelihoods, which makes inference challenging. Here we address this obstacle by introducing a fast, approximate inference method for non-conjugate GPFA models. Our approach uses orthogonal second-order polynomials to approximate the nonlinear terms in the non-conjugate log-likelihood, resulting in a method we refer to as polynomial approximate log-likelihood (PAL) estimators. This approximation allows for accurate closed-form evaluation of marginal likelihood and fast numerical optimization for parameters and hyperparameters. We derive PAL estimators for GPFA models with binomial, Poisson, and negative binomial observations, and additionally show that the parameters obtained can be used to initialize black-box variational inference, which significantly speeds up and stabilizes the inference procedure for these factor analytic models. We apply these methods to data from mouse visual cortex and monkey higher-order visual and parietal cortices, and compare GPFA under three different spike count observation models to traditional GPFA. We demonstrate that PAL estimators achieve fast and accurate extraction of latent structure from multi-neuron spike train data.

Minimax linkage was first introduced by Ao et al. [3] in 2004, as an alternative to standard linkage methods used in hierarchical clustering. Minimax linkage relies on distances to a prototype for each cluster; this prototype can be thought of as a representative object in the cluster, hence improving the interpretability of clustering results. Bien and Tibshirani analyzed properties of this method in 2011 [2], popularizing the method within the statistics community. Additionally, they performed comparisons of minimax linkage to standard linkage methods, making use of five data sets and two different evaluation metrics (distance to prototype and misclassification rate). In an effort to expand upon their work and evaluate minimax linkage more comprehensively, our benchmark study focuses on thorough method evaluation via multiple performance metrics on several well-described data sets. We also make all code and data publicly available through an R package, for full reproducibility. Similarly to [2], we find that minimax linkage often produces the smallest maximum minimax radius of all linkage methods, meaning that minimax linkage produces clusters where objects in a cluster are tightly clustered around their prototype. This is true across a range of values for the total number of clusters (k). However, this is not always the case, and special attention should be paid to the case when k is the true known value. For true k, minimax linkage does not always perform the best in terms of all the evaluation metrics studied, including maximum minimax radius. This paper was motivated by the IFCS Cluster Benchmarking Task Force's call for clustering benchmark studies and the white paper [5], which put forth guidelines and principles for comprehensive benchmarking in clustering. Our work is designed to be a neutral benchmark study of minimax linkage.