In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: We first consider the problem of learning k-parities in the on-line mistake-bound model: given a hidden vector x ∈ {0, 1} with |x| = k and a sequence of “questions” a1, a2, · · · ∈ {0, 1} , where the algorithm must reply to each question with 〈ai, x〉 (mod 2), what is the best tradeoff between the number of mistakes made by the algorithm and its time complexity? We improve the previous best result of Buhrman et. al. [BGM10] by an exp(k) factor in the time complexity. Second, we consider the problem of learning k-parities in the presence of classification noise of rate η ∈ (0, 1/2). A polynomial time algorithm for this problem (when η > 0 and k = ω(1)) is a longstanding challenge in learning theory. Grigorescu et al. [GRV11] showed an algorithm running in time ( n k/2 )1+4η+o(1) . Note that this algorithm inherently requires time ( n k/2 ) even when the noise rate η is polynomially small. We observe that for sufficiently small noise rate, it is possible to break the ( n k/2 ) barrier. In particular, if for some function f(n) = ω(1) and α ∈ [1/2, 1), k = n/f(n) and η = o(f(n)/ log n), then there is an algorithm for the problem with running time poly(n) · ( n k )1−α · e.

A: On learning k-parities with and without noise
****
Q: This paper concerns the probabilistic evalu­ ation of the effects of actions in the presence of unmeasured variables. We show that the identification of causal effect between a sin­ gleton variable X and a set of variables Y can be accomplished systematically, in time polynomial in the number of variables in the graph. When the causal effect is identifiable, a closed-form expression can be obtained for the probability that the action will achieve a specified goal, or a set of goals.

A: Testing Identifiability of Causal Effects
****
Q: In Computer Vision, problem of identifying or classifying the objects present in an image is called Object Categorization. It is a challenging problem, especially when the images have clutter background, occlusions or different lighting conditions. Many vision features have been proposed which aid object categorization even in such adverse conditions. Past research has shown that, employing multiple features rather than any single features leads to better recognition. Multiple Kernel Learning (MKL) framework has been developed for learning an optimal combination of features for object categorization. Existing MKL methods use linear combination of base kernels which may not be optimal for object categorization. Real-world object categorization may need to consider complex combination of kernels(non-linear) and not only linear combination. Evolving non-linear functions of base kernels using Genetic Programming is proposed in this report. Experiment results show that non-kernel generated using genetic programming gives good accuracy as compared to linear combination of kernels.

A:
Finding Optimal Combination of Kernels using Genetic Programming
****