图形模型入门：Michael Jordan与Kevin P. Murphy

4星 · 超过85%的资源需积分: 10 156 浏览量更新于2024-07-31 1 收藏 6.65MB PDF 举报

"《图形模型入门》迈克尔·乔丹" 本书是对图形模型的入门介绍，作者凯文·P·墨菲在2001年5月10日撰写，旨在帮助读者理解这一领域的基本概念。图形模型是概率论与图论的结合，主要解决实际应用中的不确定性与复杂性问题，尤其在机器学习算法的设计和分析中发挥着日益重要的作用。图形模型的核心思想是模块化，即将复杂的系统通过组合更简单的部分来构建。概率论提供了连接这些部分的粘合剂，确保整体的一致性，并提供了模型与数据交互的方法。而图论方面，图形模型提供了直观的界面，使得人类可以方便地对高度相互作用的变量集合建模，同时也为设计高效通用的算法提供了数据结构支持。书中涵盖了许多经典的多元概率系统，如贝叶斯网络、马尔可夫随机场等。这些模型能够有效地表示变量之间的条件依赖关系，帮助我们理解和处理高维数据中的复杂关系。例如，贝叶斯网络利用有向无环图（DAG）来描述随机变量间的因果关系，通过先验概率和观测数据更新后验概率，进行推理和决策。而马尔可夫随机场（Markov Random Field, MRF）则采用无向图来表示变量间的统计独立性假设，其能量函数用于量化变量配置的合理性。在机器学习中，图形模型被广泛应用于特征选择、模型降维、分类、回归、异常检测以及推荐系统等多个任务。例如，通过利用图形模型，我们可以更高效地推断隐藏变量，进行联合概率估计，或者在大规模数据集上进行近似推理。此外，图形模型还涉及到最大似然估计、最大后验概率（MAP）求解、消息传递算法（如信念传播和变量消元）、 EM（期望最大化）算法等统计学习方法。这些方法不仅在理论上有深厚的基础，而且在实际应用中具有很高的实用价值。《图形模型入门》是一本深入浅出的教材，它将理论与实践相结合，帮助读者掌握图形模型这一强大的工具，以便更好地应对实际问题中的不确定性和复杂性挑战。无论是对概率论和图论感兴趣的学生，还是希望在机器学习领域深化研究的从业者，这本书都是不可或缺的参考资料。

The standard approach is to keep adding hidden nodes one at a time, performing structure learning at each

step, until the score drops. There has been some recent work on more intelligent heuristics. For example,

dense clique-like graphs (such as that in Figure 9(b)) suggest that a hidden node should be added [ELFK00].

5 Decision making under uncertainty

It is sometimes said that “Decision Theory = Probability Theory + Utility Theory” [DW91, RN95]. We

have outlined above how we can model joint probability distributions in a compact way by using sparse

graphs to reﬂect conditional independence relationships. It is also possible to decompose multi-attribute

utility functions in a similar way. Let the global utility be a sum of local utilities, U =

i=1

. We create

a node for each U

term, which has as parents all the attributes (random variables) on which it depends;

typically, the utility nodes will also have action (control) nodes as parents, since the utility depends both on

the state of the world and the action we perform. The resulting graph is called an inﬂuence diagram. We

can then use algorithms, similar to the inference algorithms discussed in Section 3, to compute the optimal

(sequence of) action(s) to perform so as to maximimize expected utility [CDLS99]. (See [KLS01] for a recent

application of this to multi-person game theory.)

In sequential decision theory, the agent (decision maker) is assumed to be interacting with the environment

which is modelled as a dynamical system (see Figure 5(a)). If this dynamical system is linear with Gaussian

noise, and the utility function is negative quadratic loss

, then techniques from control theory can be used to

compute the optimal policy, i.e., mapping from percepts to actions. If the system is non-linear, the standard

approach is to locally linearize the system.

Linear dynamical systems (LDSs) enjoy the separation property, which states that the optimal behavior can

be obtained by ﬁrst doing state estimation (i.e., infer the hidden states), and then using the expected value

of the hidden states as input to a regular LQG (linear quadratic Gaussian) controller. In general, however,

the separation property does not hold. For example, consider controlling a mobile robot. The optimal action

should take into account the robot’s uncertainty about the state of the world (e.g., its location), and not

just use the mode of the posterior as if it were the true state of the world. The latter strategy (which is

called a certainty-equivalent controller) would never perform information-gathering moves. In other words,

the robot might not choose to look before it leapt, no matter how uncertain it was.

In general, ﬁnding good controllers for non-linear, partially observed systems, usually with unknown parame-

ters, is extremely challenging. One approach that shows some promise is reinforcement learning. Most of the

work has been on systems which are fully observed (e.g., [SB98]), but there has been some work on partially

observed systems (e.g., [KLC98]). Recent policy search methods (e.g., [NJ00]) show particular promise.

6 Applications

Special cases of Bayes nets were independently invented by many diﬀerent communities many years ago,

e.g., genetics (linkage analysis), speech recognition (HMMs), tracking (Kalman ﬁtering), data compression

(density estimation), channel coding (turbocodes), etc.

The general framework was developed by Pearl [Pea88] and various European researchers [JLO90, CDLS99],

who used it to make probabilistic expert systems. Many of these systems were used for medical diagnosis.

For example, consider a missile tracking an airplane, where the goal is to minimize the squared distance between itself and

the target.

The same kind of diagnosis technology has since been widely adopted by Microsoft, e.g., the Answer Wizard

of Oﬃce 95, the Oﬃce Assistant (the bouncy paperclip guy) of Oﬃce 97, and over 30 technical support

troubleshooters. In fact, Microsoft now oﬀers a Bayesian network API for Windows developers.

Another interesting ﬁelded application is the Vista system, developed by Eric Horvitz. The Vista system

is a decision-theoretic system that has been used at NASA Mission Control Center in Houston for several

years. The system uses Bayesian networks to interpret live telemetry and provides advice on the likelihood

of alternative failures of the space shuttle’s propulsion systems. It also considers time criticality and recom-

mends actions of the highest expected utility. The Vista system also employs decision-theoretic methods for

controlling the display of information to dynamically identify the most important information to highlight.

Horvitz has gone on to attempt to apply similar technology to Microsoft products, e.g., the Lumiere user

interface project [HBH

98].

7 Acknowledgements

I would like to thank Charles Twardy for comments on this manuscript.

References

[AM00] S. M. Aji and R. J. McEliece. The generalized distributive law. IEEE Trans. Info. Theory,

46(2):325–343, March 2000.

[Att98] H. Attias. Independent factor analysis. Neural Computation, 1998. In Press.

[Bun94] W. L. Buntine. Operations for learning with graphical models. J. of AI Research, pages 159–225,

1994.

[Bun96] W. Buntine. A guide to the literature on learning probabilistic networks from data. IEEE Trans.

on Knowledge and Data Engineering, 8(2), 1996.

[CDLS99] R. G. Cowell, A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter. Probabilistic Networks and

Expert Systems. Springer, 1999.

[CH97] D. Chickering and D. Heckerman. Eﬃcient approximations for the marginal likelihood of incom-

plete data given a Bayesian network. Machine Learning, 29:181–212, 1997.

[DW91] T. Dean and M. Wellman. Planning and Control. Morgan Kaufmann, 1991.

[ELFK00] G. Elidan, N. Lotner, N. Friedman, and D. Koller. Discovering hidden variables: A structure-

based approach. In Advances in Neural Info. Proc. Systems, 2000.

[FP00] W. T. Freeman and E. C. Pasztor. Markov networks for super-resolution. In Proc. 34th Annual

Conf. on Information Sciences and Systems (CISS 2000), 2000.

[FPC00] W. T. Freeman, E. C. Pasztor, and O. T. Carmichael. Learning low-level vision. Intl. J. Computer

Vision, 2000.

[Fri97] N. Friedman. Learning Bayesian networks in the presence of missing values and hidden variables.

In Proc. of the Conf. on Uncertainty in AI, 1997.

[FW00] W. Freeman and Y. Weiss. On the ﬁxed points of the max-product algorithm. IEEE Trans. on

Info. Theory, 2000. To appear.

[GC99] C. Glymour and G. Cooper, editors. Computation, Causation and Discovery. MIT Press, 1999.

[GG84] S. Geman and D. Geman. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration

of images. IEEE Trans. on Pattern Analysis and Machine Intelligence, 6(6), 1984.

[GRS96] W. Gilks, S. Richardson, and D. Spiegelhalter. Markov Chain Monte Carlo in Practice. Chapman

and Hall, 1996.

[HBH

98] E. Horvitz, J. Breese, D. Heckerman, D. Hovel, and K. Rommelse. The lumiere project: Bayesian

user modeling for inferring the goals and needs of software users. In Proc. of the Conf. on

Uncertainty in AI, 1998.

[HD96] C. Huang and A. Darwiche. Inference in belief networks: A procedural guide. Intl. J. Approx.

Reasoning, 15(3):225–263, 1996.

[Hec98] D. Heckerman. A tutorial on learning with Bayesian networks. In M. Jordan, editor, Learning in

Graphical Models. MIT Press, 1998.

[JGJS98] M. I. Jordan, Z. Ghahramani, T. S. Jaakkola, and L. K. Saul. An introduction to variational

methods for graphical models. In M. Jordan, editor, Learning in Graphical Models. MIT Press,

1998.

[JLO90] F. Jensen, S. L. Lauritzen, and K. G. Olesen. Bayesian updating in causal probabilistic networks

by local computations. Computational Statistics Quarterly, 4:269–282, 1990.

[Jor99] M. I. Jordan, editor. Learning in Graphical Models. MIT Press, 1999.

[JP95] R. Jirousek and S. Preucil. On the eﬀective implementation of the iterative proportional ﬁtting

procedure. Computational Statistics & Data Analysis, 19:177–189, 1995.

[KLC98] L. P. Kaelbling, M. Littman, and A. Cassandra. Planning and acting in partially observable

stochastic domains. Artiﬁcial Intelligence, 101, 1998.

[KLS01] M. Kearns, M. Littman, and S. Singh. Graphical models for game theory. In Proc. of the Conf.

on Uncertainty in AI, 2001.

[Mac95] D. MacKay. Probable networks and plausible predictions — a review of practical Bayesian

methods for supervised neural networks. Network, 1995.

[MMC98] R. J. McEliece, D. J. C. MacKay, and J. F. Cheng. Turbo decoding as an instance of Pearl’s

’belief propagation’ algorithm. IEEE J. on Selected Areas in Comm., 16(2):140–152, 1998.

[Mur01] K. Murphy. Learning Bayes net structure from sparse data sets. Technical report, Comp. Sci.

Div., UC Berkeley, 2001.

[MWJ99] K. Murphy, Y. Weiss, and M. Jordan. Loopy belief propagation for approximate inference: an

empirical study. In Proc. of the Conf. on Uncertainty in AI, 1999.

[NJ00] A. Ng and M. Jordan. PEGASUS: A policy search method for large MDPs and POMDPs. In

Proc. of the Conf. on Uncertainty in AI, 2000.

[Pea88] J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan

Kaufmann, 1988.

[Pea00] J. Pearl. Causality: Models, Reasoning and Inference. Cambridge Univ. Press, 2000.

[PS91] M. Peot and R. Shachter. Fusion and propogation with multiple observations in belief networks.

Artiﬁcial Intelligence, 48:299–318, 1991.

剩余520页未读，继续阅读

xforcex

粉丝: 0
资源: 1

图形模型入门：Michael Jordan与Kevin P. Murphy

an introduction to probabilistic graphical models by Michael Jordan

An introduction to probabilistic graphical models

Introduction to Graphical Models

An Introduction to Probabilistic Graphical Models

Introduction to Graphical Model

图形模型入门：Michael I. Jordan的视角

jsp物流信息网建设(源代码+论文)(2024vl).7z

中小学教师教育教学情况调查表（学生家长用）.docx

航空车辆检测8-YOLO（v5至v11）、COCO、CreateML、Paligemma、TFRecord、VOC数据集合集.rar

LabVIEW实现NB-IoT通信【LabVIEW物联网实战】

最新资源