Linear Discriminant Analysis (LDA) is a well-known method for dimension reduction and classification with focus on discriminative feature selection. However, how to discover discriminative as well as representative features in LDA model has not been explored. In this paper, we propose a latent Fisher discriminant model with representative feature discovery in an semi-supervised manner. Specifically, our model leverages advantages of both discriminative and generative models by generalizing LDA with data-driven prior over the latent variables. Thus, our method combines multi-class, latent variables and dimension reduction in an unified Bayesian framework. We test our method on MUSK and Corel datasets and yield competitive results compared to baselines. We also demonstrate its capacity on the challenging TRECVID MED11 dataset for semantic keyframe extraction and conduct a human-factors ranking-based experimental evaluation, which clearly demonstrates our proposed method consistently extracts more semantically meaningful keyframes than challenging baselines.

We address the problem of general function release under differential privacy, by developing a functional mechanism that applies under the weak assumptions of oracle access to target function evaluation and sensitivity. These conditions permit treatment of functions described explicitly or implicitly as algorithmic black boxes. We achieve this result by leveraging the iterated Bernstein operator for polynomial approximation of the target function, and polynomial coefficient perturbation. Under weak regularity conditions, we establish fast rates on utility measured by high-probability uniform approximation. We provide a lower bound on the utility achievable for any functional mechanism that is epsilon-differentially private. The generality of our mechanism is demonstrated by the analysis of a number of example learners, including naive Bayes, non-parametric estimators and regularized empirical risk minimization. Competitive rates are demonstrated for kernel density estimation; and epsilon-differential privacy is achieved for a broader class of support vector machines than known previously.

We present new algorithms for learning Bayesian networks from data with missing values using a data augmentation approach. An exact Bayesian network learning algorithm is obtained by recasting the problem into a standard Bayesian network learning problem without missing data. As expected, the exact algorithm does not scale to large domains. We build on the exact method to create an approximate algorithm using a hill-climbing technique. This algorithm scales to large domains so long as a suitable standard structure learning method for complete data is available. We perform a wide range of experiments to demonstrate the benefits of learning Bayesian networks with such new approach.

We examine the surveying problem, where we attempt to predict how a target user is likely to respond to questions by iteratively querying that user, collaboratively based on the responses of a sample set of users. We focus on an active learning approach, where the next question we select to ask the user depends on their responses to the previous questions. We propose a method for solving the problem based on a Bayesian dimensionality reduction technique. We empirically evaluate our method, contrasting it to benchmark approaches based on augmented linear regression, and show that it achieves much better predictive performance, and is much more robust when there is missing data.

Visual sentiment analysis is raising more and more attention with the increasing tendency to express emotions through images. While most existing works assign a single dominant emotion to each image, we address the sentiment ambiguity by label distribution learning (LDL), which is motivated by the fact that image usually evokes multiple emotions. Two new algorithms are developed based on conditional probability neural network (CPNN). First, we proposed BCPNN which encodes image label into a binary representation to replace the signless integers used in CPNN, and employ it as a part of input for the neural network. Then, we train our ACPNN model by adding noises to ground truth label and augmenting affective distributions. Since current datasets are mostly annotated for single-label learning, we build two new datasets, one of which is relabeled on the popular Flickr dataset and the other is collected from Twitter. These datasets contain 20,745 images with multiple affective labels, which are over ten times larger than the existing ones. Experimental results show that the proposed methods outperform the state-of-the-art works on our large-scale datasets and other publicly available benchmarks.

Speech interaction systems have been gaining popularity in recent years. The main purpose of these systems is to generate more satisfactory responses according to users' speech utterances, in which the most critical problem is to analyze user intention. Researches show that user intention conveyed through speech is not only expressed by content, but also closely related with users' speaking manners (e.g. with or without acoustic emphasis). How to incorporate these heterogeneous attributes to infer user intention remains an open problem. In this paper, we define Intention Prominence (IP) as the semantic combination of focus by text and emphasis by speech, and propose a multi-task deep learning framework to predict IP. Specifically, we first use long short-term memory (LSTM) which is capable of modeling long short-term contextual dependencies to detect focus and emphasis, and incorporate the tasks for focus and emphasis detection with multi-task learning (MTL) to reinforce the performance of each other. We then employ Bayesian network (BN) to incorporate multimodal features (focus, emphasis, and location reflecting users' dialect conventions) to predict IP based on feature correlations. Experiments on a data set of 135,566 utterances collected from real-world Sogou Voice Assistant illustrate that our method can outperform the comparison methods over 6.9-24.5% in terms of F1-measure. Moreover, a real practice in the Sogou Voice Assistant indicates that our method can improve the performance on user intention understanding by 7%.

We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanation to the Bayesian Occam's razor criteria, under the assumption that the data is generated by an i.i.d distribution. Moreover, as the negative log-likelihood is an unbounded loss function, we motivate and propose a PAC-Bayesian theorem tailored for the sub-gamma loss family, and we show that our approach is sound on classical Bayesian linear regression tasks.

We study the performance of data-driven, a priori and random approaches to label space partitioning for multi-label classification with a Gaussian Naive Bayes classifier. Experiments were performed on 12 benchmark data sets and evaluated on 5 established measures of classification quality: micro and macro averaged F1 score, Subset Accuracy and Hamming loss. Data-driven methods are significantly better than an average run of the random baseline. In case of F1 scores and Subset Accuracy - data driven approaches were more likely to perform better than random approaches than otherwise in the worst case. There always exists a method that performs better than a priori methods in the worst case. The advantage of data-driven methods against a priori methods with a weak classifier is lesser than when tree classifiers are used.

Two fundamental problems in computational game theory are computing a Nash equilibrium and learning to exploit opponents given observations of their play (opponent exploitation). The latter is perhaps even more important than the former: Nash equilibrium does not have a compelling theoretical justification in game classes other than two-player zero-sum, and for all games one can potentially do better by exploiting perceived weaknesses of the opponent than by following a static equilibrium strategy throughout the match. The natural setting for opponent exploitation is the Bayesian setting where we have a prior model that is integrated with observations to create a posterior opponent model that we respond to. The most natural, and a well-studied prior distribution is the Dirichlet distribution. An exact polynomial-time algorithm is known for best-responding to the posterior distribution for an opponent assuming a Dirichlet prior with multinomial sampling in normal-form games; however, for imperfect-information games the best known algorithm is based on approximating an infinite integral without theoretical guarantees. We present the first exact algorithm for a natural class of imperfect-information games. We demonstrate that our algorithm runs quickly in practice and outperforms the best prior approaches. We also present an algorithm for the uniform prior setting.

Our learning task: Given a training set S {(x1 , y1), (x2 , y2), . . . The simplest case: y { 1, 1} called binary classification problem If y is a real number it becomes a regression problem More general case, y can be a vector and each element is drawn from a finite set.