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view toolboxes/FullBNT-1.0.7/bnt/CPDs/@softmax_CPD/softmax_CPD.m @ 0:e9a9cd732c1e tip
first hg version after svn
author | wolffd |
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date | Tue, 10 Feb 2015 15:05:51 +0000 |
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function CPD = softmax_CPD(bnet, self, varargin) % SOFTMAX_CPD Make a softmax (multinomial logit) CPD % % To define this CPD precisely, let W be an (m x n) matrix with W(i,:) = {i-th row of B} % => we can define the following vectorial function: % % softmax: R^n |--> R^m % softmax(z,i-th)=exp(W(i,:)*z)/sum_k(exp(W(k,:)*z)) % % (this constructor augments z with a one at the beginning to introduce an offset term (=bias, intercept)) % Now call the continuous (cts) and always observed (obs) parents X, % the discrete parents (if any) Q, and this node Y then we use the discrete parent(s) just to index % the parameter vectors (c.f., conditional Gaussian nodes); that is: % prob(Y=i | X=x, Q=j) = softmax(x,i-th|j) % where '|j' means that we are using the j-th (m x n) parameters matrix W(:,:,j). % If there are no discrete parents, this is a regular softmax node. % If Y is binary, this is a logistic (sigmoid) function. % % CPD = softmax_CPD(bnet, node_num, ...) will create a softmax CPD with random parameters, % where node is the number of a node in this equivalence class. % % The following optional arguments can be specified in the form of name/value pairs: % [default value in brackets] % (Let ns(i) be the size of node i, X = ns(X), Y = ns(Y), Q1=ns(dps(1)), Q2=ns(dps(2)), ... % where dps are the discrete parents; if there are no discrete parents, we set Q1=1.) % % discrete - the discrete parents that we want to treat like the cts ones [ [] ]. % This can be used to define sigmoid belief network - see below the reference. % For example suppose that Y has one cts parents X and two discrete ones: Q, C1 where: % -> Q is binary (1/2) and used just to index the parameters of 'self' % -> C1 is ternary (1/2/3) and treated as a cts node <=> its values appear into the linear % part of the softmax function % then: % prob(Y|X=x, Q=q, C1=c1)= softmax(W(:,:,q)' * y) % where y = [1 | delta(C1,1) delta(C1,2) delta(C1,3) | x(:)']' and delta(Y,a)=indicator(Y=a). % weights - (w(:,j,a,b,...) - w(:,j',a,b,...)) is ppn to dec. boundary % between j,j' given Q1=a,Q2=b,... [ randn(X,Y,Q1,Q2,...) ] % offset - (b(j,a,b,...) - b(j',a,b,...)) is the offset to dec. boundary % between j,j' given Q1=a,Q2=b,... [ randn(Y,Q1,Q2,...) ] % % e.g., CPD = softmax_CPD(bnet, i, 'offset', zeros(ns(i),1)); % % The following fields control the behavior of the M step, which uses % a weighted version of the Iteratively Reweighted Least Squares (WIRLS) if dps_as_cps=[]; or % a weighted SCG otherwise, as implemented in Netlab, and modified by Pierpaolo Brutti. % % clamped - 'yes' means don't adjust params during learning ['no'] % max_iter - the maximum number of steps to take [10] % verbose - 'yes' means print the LL at each step of IRLS ['no'] % wthresh - convergence threshold for weights [1e-2] % llthresh - convergence threshold for log likelihood [1e-2] % approx_hess - 'yes' means approximate the Hessian for speed ['no'] % % For backwards compatibility with BNT2, you can also specify the parameters in the following order % softmax_CPD(bnet, self, w, b, clamped, max_iter, verbose, wthresh, llthresh, approx_hess) % % REFERENCE % For details on the sigmoid belief nets, see: % - Neal (1992). Connectionist learning of belief networks, Artificial Intelligence, 56, 71-113. % - Saul, Jakkola, Jordan (1996). Mean field theory for sigmoid belief networks, Journal of Artificial Intelligence Reseach (4), pagg. 61-76. % % For details on the M step, see: % - K. Chen, L. Xu, H. Chi (1999). Improved learning algorithms for mixtures of experts in multiclass % classification. Neural Networks 12, pp. 1229-1252. % - M.I. Jordan, R.A. Jacobs (1994). Hierarchical Mixtures of Experts and the EM algorithm. % Neural Computation 6, pp. 181-214. % - S.R. Waterhouse, A.J. Robinson (1994). Classification Using Hierarchical Mixtures of Experts. In Proc. IEEE % Workshop on Neural Network for Signal Processing IV, pp. 177-186 if nargin==0 % This occurs if we are trying to load an object from a file. CPD = init_fields; CPD = class(CPD, 'softmax_CPD', discrete_CPD(0, [])); return; elseif isa(bnet, 'softmax_CPD') % This might occur if we are copying an object. CPD = bnet; return; end CPD = init_fields; assert(myismember(self, bnet.dnodes)); ns = bnet.node_sizes; ps = parents(bnet.dag, self); dps = myintersect(ps, bnet.dnodes); cps = myintersect(ps, bnet.cnodes); clamped = 0; CPD = class(CPD, 'softmax_CPD', discrete_CPD(clamped, ns([ps self]))); dps_as_cpssz = 0; dps_as_cps = []; % determine if any discrete parents are to be treated as cts if nargin >= 3 & isstr(varargin{1}) % might have passed in 'discrete' for i=1:2:length(varargin) if strcmp(varargin{i}, 'discrete') dps_as_cps = varargin{i+1}; assert(myismember(dps_as_cps, dps)); dps = mysetdiff(dps, dps_as_cps); % put out the dps treated as cts CPD.dps_as_cps.ndx = find_equiv_posns(dps_as_cps, ps); CPD.dps_as_cps.separator = [0 cumsum(ns(dps_as_cps(1:end-1)))]; % concatenated dps_as_cps dims separators dps_as_cpssz = sum(ns(dps_as_cps)); break; end end end assert(~isempty(union(cps, dps_as_cps))); % It have to be at least a cts or a dps_as_cps parents self_size = ns(self); cpsz = sum(ns(cps)); glimsz = prod(ns(dps)); CPD.dpndx = find_equiv_posns(dps, ps); % it contains only the indeces of the 'pure' dps CPD.cpndx = find_equiv_posns(cps, ps); CPD.self = self; CPD.solo = (length(ns)<=2); CPD.sizes = bnet.node_sizes([ps self]); % set default params CPD.max_iter = 10; CPD.verbose = 0; CPD.wthresh = 1e-2; CPD.llthresh = 1e-2; CPD.approx_hess = 0; CPD.glim = cell(1,glimsz); for i=1:glimsz CPD.glim{i} = glm(dps_as_cpssz + cpsz, self_size, 'softmax'); end if nargin >= 3 args = varargin; nargs = length(args); if ~isstr(args{1}) % softmax_CPD(bnet, self, w, b, clamped, max_iter, verbose, wthresh, llthresh, approx_hess) if nargs >= 1 & ~isempty(args{1}), CPD = set_fields(CPD, 'weights', args{1}); end if nargs >= 2 & ~isempty(args{2}), CPD = set_fields(CPD, 'offset', args{2}); end if nargs >= 3 & ~isempty(args{3}), CPD = set_clamped(CPD, args{3}); end if nargs >= 4 & ~isempty(args{4}), CPD.max_iter = args{4}; end if nargs >= 5 & ~isempty(args{5}), CPD.verbose = args{5}; end if nargs >= 6 & ~isempty(args{6}), CPD.wthresh = args{6}; end if nargs >= 7 & ~isempty(args{7}), CPD.llthresh = args{7}; end if nargs >= 8 & ~isempty(args{8}), CPD.approx_hess = args{8}; end else CPD = set_fields(CPD, args{:}); end end % sufficient statistics % Since dsoftmax is not in the exponential family, we must store all the raw data. CPD.parent_vals = []; % X(l,:) = value of cts parents in l'th example CPD.self_vals = []; % Y(l,:) = value of self in l'th example CPD.eso_weights=[]; % weights used by the WIRLS algorithm % For BIC CPD.nsamples = 0; if ~adjustable_CPD(CPD), CPD.nparams=0; else [W, b] = extract_params(CPD); CPD.nparams= prod(size(W)) + prod(size(b)); end %%%%%%%%%%% function CPD = init_fields() % This ensures we define the fields in the same order % no matter whether we load an object from a file, % or create it from scratch. (Matlab requires this.) CPD.glim = {}; CPD.self = []; CPD.solo = []; CPD.max_iter = []; CPD.verbose = []; CPD.wthresh = []; CPD.llthresh = []; CPD.approx_hess = []; CPD.sizes = []; CPD.parent_vals = []; CPD.eso_weights=[]; CPD.self_vals = []; CPD.nsamples = []; CPD.nparams = []; CPD.dpndx = []; CPD.cpndx = []; CPD.dps_as_cps.ndx = []; CPD.dps_as_cps.separator = [];