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.

Input: Consider Input: Bayesian networks can be used to extract explanations about the observed state of a subset of variables. In this paper, we explicate the desiderata of an explanation and confront them with the concept of explanation proposed by existing methods. The necessity of taking into account causal approaches when a causal graph is available is discussed. We then introduce causal explanation trees, based on the construction of explanation trees using the measure of causal information ow (Ay and Polani, 2006). This approach is compared to several other methods on known networks.

Output: Explanation Trees for Causal Bayesian Networks


Input: Consider Input: Self-paced learning (SPL) has been attracting increasing attention in machine learning and computer vision. Albeit empirically substantiated to be effective, the investigation on its theoretical insight is still a blank. It is even unknown that what objective a general SPL regime converges to. To this issue, this study attempts to initially provide some new insights under this “heuristic” learning scheme. Specifically, we prove that the solving strategy on SPL exactly accords with a majorization minimization algorithm, a well known technique in optimization and machine learning, implemented on a latent objective. A more interesting finding is that, the loss function contained in this latent objective has a similar configuration with non-convex regularized penalty, an attractive topic in statistics and machine learning. In particular, we show that the previous hard and linear self-paced regularizers are equivalent to the capped norm and minimax concave plus penalties, respectively, both being widely investigated in statistics. Such connections between SPL and previous known researches enhance new insightful comprehension on SPL, like convergence and parameter setting rationality. The correctness of the proposed theory is substantiated by experimental results on synthetic and UCI data sets.

Output: What Objective Does Self-paced Learning Indeed Optimize?


Input: Consider Input: We discuss the problem of construction of inference procedures which can manipulate with uncertainties measured in ordinal scales and fulfil to the property of strict monotonic­ ity of conclusion. The class of A-valuations of plausibility is considered where operations based only on information about linear or­ dering of plausibility values are used. In this class the modus ponens generating function fulfiling to the property of strict monotonic­ ity of conclusions is introduced. 1 STABILITY OF DECISIONS IN INFERENCE PROCEDURES Human judgements about plausibility, truth, certainty values of premises, rules and facts are usually qualita­ tive and measured in ordinal scales. Representation of these judgements by numbers from interval L = [0, lJ or L = [0, 100] and using over these numbers quanti­ tative operations such as multiplication, addition and so on is not always correct. Let's consider example. Let R1 and R2 are two rules of some expert system: Rl: If At then H1,pv(RI), (1) R2: If A2 then H2,pv(R2), (2) where pv(RI) and pv(R2) are the plausibility, cer­ tainty, truth values of rules measured in some linearly ordered scale L, for example L = [0, 1]. Often plausi­ bilities of conclusions are calculated by: pv(Ht) = pv(Rl) * pv(At), (3) pv(H2) = pv(R2) * pv(A2), (4) where pv(At) and pv(A2} are the plausibilities of premises and * is some T-norm, for example multi­ plication operation (Godo, Lopez de Mantaras et al. 1988; Hall1990; Trillas, Valverde 1985; Valverde, Tril­ las 1985; Forsyth 1984). Generally the plausibility of conclusion can be calculated by means of a modus po­ nens generating function mpgf: pv(HI) = mpgf(p·v(At),pv(Rt)). Let in (1)-( 4) the qualitative information about plau­ sibility values is the next: pv(At) < pv(A2} < pv(R2) < pv(RI), (5) that is the plausibility values of premises are less than the plausibility values of rules, the plausibility value of A1 is less than the plausibility value of A2 and the plausibility value of rule R2 is less than the plausibility value of rule Rl. Let these plausibility values are inter­ preted as the next quantitative values from L = (0, 1]: pv(A1) = 0.3 < pv(A2) = 0. 4 < pv(R2} = 0.6 <


Output: Modus Ponens Generating Function in the Class of A-valuations of Plausibility